From Brownian to Driven and Active Dynamics of Colloids...

From Brownian to Driven and Active Dynamics of Colloids

Energetics and FluctuationsPart I

Masaki Sano

Department of Physics

The University of Tokyo

IAS Program on Frontiers of Soft Matter Physics Tutorial

Outline of Talk

bull Introduction to Brownian motion Fluctuation Dissipation Theorem

bull Stochastic Energetics (by K Sekimoto 1997)

bull Fluctuation Theorems Jarzynski Equality etc (1993-1996) rarr (Tuesday by Hyunggyu Park)

bull Measuring energy dissipation in small systems

bull Information Feedback control and thermodynamics

bull Self-propelled particles Active Matter

Part I

Part II

Einsteinrsquos Derivation of the Relation for Brownian Motion

bull Consider colloidal suspension in an equilibrium state under the balance between external field and diffusion

120588119907119891

120588(119909) Concentration gradient

120588119892

120588(119911)minus119863

119889120588

119889119909

minus120574119863119889120588

119889119911Current by diffusion

Current by external force

Under gravity

Total current

Equilibrium condition

(1)

bull Osmotic pressure due to particle concentration

bull Force due to osmotic pressure balances with the external force f

Stokesrsquos law of drag force

Drag coefficient

(2)

From eq (1) and (2)

Einstein-Stokes Relation

Mesoscopic relation connecting between atomic scale and macroscopic scale

Brownian motion and Langevin equation

bull Langevin equation

Integrating this equation

Multiplying v(t) and integrating it

Using equipartition

there4

Fluctuation prop Dissipation

(1)

(2)

bull Diffusion coefficient

119863 equiv

mobility

FDT (Fluctuation Dissipation relation of 1st kind)

FDT (Fluctuation Dissipation relation of 2nd kind)

Integrating (2) gives

Theories on Non-equilibrium Systems

Classical mechanics

Newton

Quantum mechanics

ShrOumldinger

Non-equilibrium statistical mechanics

Liouville equation

BBGKY-hierarchy

Time dependent

correlation functions

Kinetic theory

Boltzmann equation

Master equation

Langevin equation

Fokker-Planck equation

Non-equilibrium

thermodynamics

Linear flux force relations

Onsager relations

Navier-Stokes equation

Particle level Particle level

Macroscopic levelMesoscopic level

Kubo

relation

Stochastic Energetics

)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt

dxdQ )( Force exerted from heat bath ｘ displacement

dWdQdE

dax

UdW

)(2

axUm

pE

by K Sekimoto JPSJ (1997)

See also Ken Sekimoto ldquoStochastic Energeticsrdquo Lecture Notes in Physics 799 (Springer)

Underdamped Langevin equation

Heat

External control parameter

Then 1 st Law of Thermodynamics holds for Langevin equations

dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW

1 st Law of Thermodynamics for Langevin Dynamics

Separate conservative forces and non-conservative forces

How to derive

Ito Integral and Stratonovich Integral in Stochastic Differential Equations

sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(

Itorsquos definition

Stratonovichrsquos defintion

Computing

t

tB BBTkdss0

02)( Wiener process Bt

Mesoscopic Nonequilibrium Systems

bull Jarzynski Equality(Relation connecting Equilibrium and Nonequilibrium )

Ex Unfolding of RNA

bull Fluctuation Theorem

（Probability of negative entropy production Proof of the second law in thermodynamics）

bull Harada-Sasa Equality

FDT violation ＝ Irreversible Production of Heat

Ex efficiency of molecular motors

processesleirreversibFW

)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results

rate productionentropy 119875(120590)

119875(minus120590)= 119890120590120591

Example Small Particle Driven by External Forces

Langevin Simulation of Active Transport ex Brownian Ratchet

Langevin Equation ( overdamped case )

0)(

)()(

txU

txUtxU

flushing

bull Energy dissipation rate (energy flow from the Brownian particle to the environment) can be defined as

according to Sekimoto(JPSJ 1997)

Energy Dissipation

But difficult to measure

Optical Trapping (LASER Tweezers)

Toyabe amp Sano (2006)

Multi-beam Laser Trap

How to make Nonequilibrium State

Switching

Swinging

Surfing

Tool Laser Tweezers and Colloid System

bull It is possible to capture and manipulate small particles

bull Particles feel harmonic potential around the focal point of the LASER

optv

x

))()(( txtxkxkF optopt

)()()( tvtFtJ optopt

dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production

Fluctuation Theorem (steady state)

functionon distributi)(

)(log

1lim

Evans et al PRL (2002)

Negative Entropy Production

Measuring Energy Dissipation in Small Systems

Harada-Sasarsquos relation PRL (2005)

Heat = Degree of Violation of FDT

TkD B )(2)( RTkC B

Correlation Function

Response Function

Equilibrium State

Einsteinrsquos Relation (1905)

The Equality is generalized for more complex systems

bull Time independent driving force with U(x)

bull Flushing potential

bull Periodically switching of potential U(xt+T)=U(xt)

bull Many particles (Colloidal suspension)

How to make Nonequilibrium Steady State (NESS)

Equilibrium Case

Check of FDT(Fluctuation Dissipation Theorem)

FDT

Shape of the potential

2654127 POINTS

Equilibrium State ( Check of Fluctuation-Dissipation Theorem )

7854 RUNS52 RUNS x 32767 POINTS

Non-Equilibrium Case

bull Flushing Switch LASER

position between two

positions temporally with

a poisson process

bull Every 10ms decide if

switch or not randomly

Measurement of Response Functions

EQ Equilibrium State

switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1

Correlation Functions amp Responses


switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1

Verification of Harada-Sasa EqualityLHS can be measured in this system

More general case (Memory effect)

)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt

Ohkuma amp T Ohta (2006)

Narayan Deutche PRE (2006)

Colloid in polymer solution viscosity has

memory effect rarr generalized Langevin

eq

Micro-RheologyMeasure viscosity from fluctuations

FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ

Molecular Rotary Motor gt F1-ATPase

bull Abrahams et al Nature(1994)

bull Noji Yasuda et al Nature(1997)

bull Yasuda Noji et al Cell(1998)

S Toyabe et al Phys Rev Lett 104 198103 (2010)

Results gt Violation of FDT

bull 04 uM ATP 04 uM ADP 1 mM Pi


Results gt Harada-Sasa equality

bull Integration Range [-300 Hz +300Hz]

bull Frictional Coefficientγ

Results gt Heat Dissipation

Error bars are SD

Energy input rate per unit time


ATPs Gv

Masaki SanoShoichi Toyabe1

Hong-ren Jiang2

Ryo Suzuki3

The University of Tokyo1Ludwig Maximilians University Munich

2National Taiwan University3Techinical University of Munich


Energetics and FluctuationsPart II


Outline of Part I

bull Stochastic Thermodynamics was introduced

bull Degree of the violation FDT relation is equal to heat flux to the environment in Langevin systems Such small heat flux can be experimentally evaluated by using a new theory

2 nd law of thermodynamics and FDT can be derived from JE

Importance of fluctuations

Small system large fluctuation

2 nd law of Thermodynamics

Maximum work

Work W

start

end

W ge F = F2 ndash F1

exp[W kT ] = exp[F kT ]

F

W

Jarzynski equality (1997）

Free Energy Ｆ

Trials

P(W)

Jarzynski Equality

Work exerted to the system

Free energy gain of the system

119882

∆119865

New Theories in Statistical Mechanics

Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2

Confirmed for driven Brownian particles electric current etc

Initial conditions producing positive entropy production is much more frequent than the negative entropy production

Evans 1993Gallavotti CohenSecond law of thermodynamics

Fluctuation dissipation theorem

Fluctuation Theorem

0

I mutual informationmeasurement and control have errors

Sagawa amp Ueda PRL (2010)119868(119860 119861)

H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868

Work performed to the system


119882

119865

Correspondingly generalized Jarzynski equality

Fluctuation Theorem Jarzynski equality

119890minus(119882minus∆119865)119896119861119879 = 1

Generalized Jarzynski equality including information

119882 minus ∆119865 ge 02nd law of thermodynamics

119890minus119909 ge 1 minus 119909

Maxwellrsquos demonbull Violation of the second law of thermodynamics

James Clerk Maxwell (1831-1879)

Opening amp closing door do not perform work to atomsrArr 2nd law really violaterArr controversial state lasted more than 150 years

47

(1871)

Maxwellrsquos Demon and Szilard Engine

WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)

The simplest and analyzable Maxwellrsquos demon

Entropy gain of gas

02ln kS

Information gain rarr decrease of entropy

Information gain ln 2

Expansion

119882

Extracted work

119882 le minus∆119865 = 0Second law requires

However we gain

Schematic illustration of the experiment

Toyabe Sagawa Ueda Muneyuki Sano Nature Physics 6 988 (2010))

Experimental Setup

Dimeric polystyrene particle (300nm) is linked on the substrate with a biotin

Particles exhibit a rotational Brownian motion

Quadrant electrodes are patterned on the substrate1 μm (11000 mm)

50

How to produce a spiral-stair-like potential

Estimating a potential function from the data

Minimize ε2

Measured potential function

Feedback control based on information contents

53

Time delay ε

Particle is observed in S

Switch

Repeat

Particle is outside of S

Do nothing

Observe position of the particle periodically

Trajectories under feedback control

54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay

Calculation of Free Energy Free energy gain

bull F

55Calculate （ΔF-W）

∆119865

+w

-w



119882

119865

Efficiency of Information-Energy Conversion

28 Efficiency

56

119868 = minus119901 ln 119901 minus 1 minus 119901 ln((1 minus 119901)

Information gained by the observation

1199011-119901

120599 =∆119865 minus119882

119896119861119879119868


bull A fundamental principle to relate energy and information feedback

bull

Experimental test of generalized Jarzynski equality

generalized Jarzynski equalitySagawa Ueda PRL (2010)

Agrees within measurement accuracy

Feedback Efficacy

- Entropy Production

57

Toyabe Sagawa Ueda Muneyuki Sano

Nature Physics 6 988 (2010))

How to measure the feedback efficacy

120574 = 119901119904119908 + 119901119899119904 lege 1

Consistency with 2nd Law

bull 2nd law holds for the total system

bull Information-energy conversion is realized when we look at the small system

Total System

59

demon Micro system

Information

Feedback

Energy Work

Self-propelled dynamics of Janus particle

bull By a local temperature gradient

Self-Thermophoresis

bull By electric field

Induced Charge Electro-Osmosis (ICEO)

Self-propulsion of Janus particle I Temperature field

ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22

HR Jiang Yoshinaga Sano PRL 105 268302 (2010)

Rotation of Chiral Doublet Thermophoresis

HR Jiang Yoshinaga Sano PRL (2010)

Temperature distribution

Seed of self-thermophoresis of Janus particle is related to the response to the external gradient

Induced flow visualized by tracer particles around the fixed Janus particle

Temperature distribution around a Janus Particle

Self-thermophoresis

Theoretical calculation by N Yoshinaga

Viewpoint in Physics PRL (2010)

Effective slip velocity

Light is absorbed on the metal side

Characteristic length

Interaction potential between the surface and fluid

Migration in an uniform external temperature gradient

Temperature diff across the particle

Migration speed is determined by the average of Soret coeff

Stochastic Dynamics of Active particle

= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for

Equilibrium distributionc

Correlation function of the polarity direction

Rotational Diffusion

MSD of active particle

Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574

Self-propulsion of Janus particle II Electric field

Motion of Janus Particle Top View

How do they move


Cross over frequency

Formation of Chains at frequency higher than fc

Doublet Triplet Linear Chain

Oscillation Wave

Fluctuation in Janus Chiral Doublet

bull How does the driving force compete with thermal fluctuations

bull Use of Fluctuation Theorem

Role of Thermal fluctuation

R Suzuki HR Jiang M Sano ArchivePrecise determination of torque is possible

Deformable self-propelled chain

Waving motion Spiraling motion

Induced Polarization

Electric charging time

Chemotaxis of Bacteria

77httpwwwsciencemagorgcontent3346053238abstract

Information and Feedback in Different Systems

Fluctuation Information Feedback Outcome

Maxwellrsquos demon Thermal Speed position Biased Choiceof fluctuations

Gain Free Energy

Active Particle Thermal ------- -------- EnhancedDiffusion

Bacteria (Escherichia coli)

tumbling Chemotactic Signal

Change tumbling freq

Chemotaxis

Amoeboid cell(DictyosteliumDiscoideum)

Instability ofcell shape

Chemotactic Signal

Biased Choice of random protrusion

Chemotaxis

78

Summary

bull Information thermodynamics can be tested and demonstrated in colloidal systems

bull Different kinds of phoresis can be used to create self-propelled particles and control interaction of particles


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II

bull Information Feedback Control and Generalized Jarzynski Equality

bull Introduction to Active particle Active Matter





Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave










Collective motion of self-propelled string

114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



Outline of Talk

bull Introduction to Brownian motion Fluctuation Dissipation Theorem

bull Stochastic Energetics (by K Sekimoto 1997)

bull Fluctuation Theorems Jarzynski Equality etc (1993-1996) rarr (Tuesday by Hyunggyu Park)

bull Measuring energy dissipation in small systems

bull Information Feedback control and thermodynamics

bull Self-propelled particles Active Matter

Part I

Part II



120588119907119891


120588119892

120588(119911)minus119863

119889120588

119889119909

minus120574119863119889120588



Under gravity

Total current


(1)




Drag coefficient

(2)

From eq (1) and (2)







Using equipartition

there4


(1)

(2)


119863 equiv

mobility





Classical mechanics

Newton

Quantum mechanics

ShrOumldinger


Liouville equation

BBGKY-hierarchy

Time dependent


Kinetic theory

Boltzmann equation

Master equation

Langevin equation


Non-equilibrium

thermodynamics


Onsager relations




Kubo

relation


)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





120588119907119891


120588119892

120588(119911)minus119863

119889120588

119889119909

minus120574119863119889120588



Under gravity

Total current


(1)




Drag coefficient

(2)

From eq (1) and (2)







Using equipartition

there4


(1)

(2)


119863 equiv

mobility





Classical mechanics

Newton

Quantum mechanics

ShrOumldinger


Liouville equation

BBGKY-hierarchy

Time dependent


Kinetic theory

Boltzmann equation

Master equation

Langevin equation


Non-equilibrium

thermodynamics


Onsager relations




Kubo

relation


)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






Drag coefficient

(2)

From eq (1) and (2)







Using equipartition

there4


(1)

(2)


119863 equiv

mobility





Classical mechanics

Newton

Quantum mechanics

ShrOumldinger


Liouville equation

BBGKY-hierarchy

Time dependent


Kinetic theory

Boltzmann equation

Master equation

Langevin equation


Non-equilibrium

thermodynamics


Onsager relations




Kubo

relation


)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II







Using equipartition

there4


(1)

(2)


119863 equiv

mobility





Classical mechanics

Newton

Quantum mechanics

ShrOumldinger


Liouville equation

BBGKY-hierarchy

Time dependent


Kinetic theory

Boltzmann equation

Master equation

Langevin equation


Non-equilibrium

thermodynamics


Onsager relations




Kubo

relation


)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




119863 equiv

mobility





Classical mechanics

Newton

Quantum mechanics

ShrOumldinger


Liouville equation

BBGKY-hierarchy

Time dependent


Kinetic theory

Boltzmann equation

Master equation

Langevin equation


Non-equilibrium

thermodynamics


Onsager relations




Kubo

relation


)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




Classical mechanics

Newton

Quantum mechanics

ShrOumldinger


Liouville equation

BBGKY-hierarchy

Time dependent


Kinetic theory

Boltzmann equation

Master equation

Langevin equation


Non-equilibrium

thermodynamics


Onsager relations




Kubo

relation


)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




)(2)()(

)()(

2

2

ttTktt

tdt

dx

x

axU

dt

xd

B

daa

UdQaxU

m

pd

)(

2

dxt

dt


dWdQdE

dax

UdW

)(2

axUm

pE




Heat



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



dax

UdU

m

pd

dax

UdUdt

m

p

dt

dpdx

x

U

dt

dpdQ

2

2

daa

UdQaxU

m

pd

)(

2

dWdQdE

)(2

axUm

pE da

x

UdW



How to derive


sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




sdBsf )(

ssss BBsfdBsf )()(

ssss BBsfssf

dBsf

2

)()()(



Computing

t

tB BBTkdss0




Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Ex Unfolding of RNA







)exp()exp( WF

(1997)

(1993-)

(2005)

Some New Results


119875(minus120590)= 119890120590120591




0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






0)(

)()(

txU

txUtxU

flushing



Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Energy Dissipation






Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II







Switching

Swinging

Surfing




optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






optv

x



dtvtFTk

opt

t

opt

B

t 0

)(1

Energy Input

Entropy production



)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





)(log

1lim






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






TkD B )(2)( RTkC B


Response Function

Equilibrium State








Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II









Equilibrium Case


FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




FDT


2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




2654127 POINTS







a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II









a poisson process





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





switching rate

NESS1 1 sec-1

NESS2 2 sec-1

NESS3 3 sec-1

NESS4 4 sec-1



)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





)(~

2)(~

)(~

)(~

)())(()()(

RkTCI

tttxFdssxstt





eq


FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




FDT

)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



)(~

2)(~

)(~

)(~

RkTCI

Left hand side

Right hand side

Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



Simplified proof

1st term

2nd term

response

)()()()(

)())()(()(

2 tvttvtJ

tdxttvdttJ













Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II















Error bars are SD



ATPs Gv


Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



Outline of Part I







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






47

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Experimental Setup




50



Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Minimize ε2



53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




53

Time delay ε


Switch

Repeat


Do nothing



54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




54

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




bull F


∆119865

+w

-w



119882

119865


28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




28 Efficiency

56



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




bull




Feedback Efficacy


57




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






Total System

59

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II









Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




How do they move





Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II







Oscillation Wave















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II

















Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

78

Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



Summary




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




Hong-ren Jiang2

Ryo Suzuki3






Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



Outline of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II







Maximum work

Work W

start

end



F

W


Free Energy Ｆ

Trials

P(W)

Jarzynski Equality



119882

∆119865


Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




Entropy production

σ

-1 -07 -0

4 -01 0

2 05 0

8 11 1

4 17

2





Fluctuation Theorem

0



H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





H(119860) H(119861)

119882 ge ∆119865 minus 119896119879 119868



119882

119865



119890minus(119882minus∆119865)119896119861119879 = 1



119890minus119909 ge 1 minus 119909




85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






85

(1871)


WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




WQ 0T

QS

(a) (b)

(d) (c)

Heat Bath

2lnTkW B

Szilard (1929)


Entropy gain of gas

02ln kS



Expansion

119882

Extracted work


However we gain



Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Experimental Setup




88



Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Minimize ε2



91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




91

Time delay ε


Switch

Repeat


Do nothing



92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




92

Time (msec)

Rev

olu

tio

ns

Time delay 120576

Up

Down

Time delay


bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




bull F


∆119865

+w

-w



119882

119865


28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




28 Efficiency

94



1199011-119901

120599 =∆119865 minus119882

119896119861119879119868



bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




bull




Feedback Efficacy


95




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




120574 = 119901119904119908 + 119901119899119904 lege 1




Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II






Total System

97

demon Micro system

Information

Feedback

Energy Work



Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II





Self-Thermophoresis




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




ttVtr

ttVtr

etVtrt

~)(

~)(

)]1([2)(

22

222

22








Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II









Self-thermophoresis











= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




= 119951 times120597

120597119951

120574119959 = minus120597119880

120597119955+ 120573119951 + 120643(119905)


Langevin equation

119951

119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



119896 = 0for





Without potential

2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



2 2 24r Dt V t

119881119868119862119864119874~1205981205761198771198642

120574



How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II




How do they move





Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II







Oscillation Wave











114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II













114






Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II








Gain Free Energy





Chemotaxis



Chemotactic Signal


Chemotaxis

116

Summary of Part II



Summary of Part II



From Brownian to Driven and Active Dynamics of Colloids...

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Transcript of From Brownian to Driven and Active Dynamics of Colloids...