The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of...
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![Page 1: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/1.jpg)
The meaning of the Second Law:Nonlocal effects in continuum physics
Peter VánBUTE, Department of Chemical Physics
– Irreversibility concepts in thermodynamics
– Stability and the Second Law
– How to construct constitutive functions?
– Example:• Ginzburg-Landau equation
![Page 2: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/2.jpg)
– ConceptsConcepts and theories– What kind of thermodynamics?
Discrete(homogeneous)
T(t)
ContinuumT(t,x)
Phenomenological(T is primitive)
Statistical(T is explained)
Equilibrium Irreversible
![Page 3: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/3.jpg)
Second Law
– time dependence – time reversal – variational principles – S exists– S is increasing – local equilibrium
Can be interpreted in a thermodynamic theory
Irreversibility
(?)
(?)
(?)
![Page 4: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/4.jpg)
Thermodynamic theory
)a(fa Dynamic law:
,...),c,v(a
1 Statics (equilibrium properties)
S
aa
S,,
T
1
e
S
2 Dynamics
0)a(f)a(DSa)a(DS)a(S
![Page 5: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/5.jpg)
1 + 2 + closed system
S is a Ljapunov function of the equilibrium of the dynamic law
Irreversibility trend to equilibrium
![Page 6: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/6.jpg)
Classical Irreversible
Thermodynamics
Local equilibrium (= there is no microstructure)
Violations (nonlocality):
•in time (memory effects)•in space (structure effects)
dynamic variables?
![Page 7: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/7.jpg)
Stability structure Dynamic structure
Example 1
)a(fa 0)( aS for all solutions of the dynamic law
)a(f)a(DS)a(S0 )a(DS)a(l)a(f
?)a(f
relaxational dynamics
![Page 8: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/8.jpg)
Example 2 (Ginzburg-Landau)
gt
0js st
),,( 2
)j,s,g( s
Liu procedure (Farkas’s lemma)
),(s (.)gs),(j(.)j 0s
0g)ss(s
)ss(.)(lgt
state space
constitutive functions
![Page 9: The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of Chemical Physics –Irreversibility concepts in thermodynamics.](https://reader036.fdocuments.in/reader036/viewer/2022071806/56649d8d5503460f94a74bb1/html5/thumbnails/9.jpg)
Conclusions
– Second Law is a stability criteria (Irreversibility is a kind of stability)
– Second Law is a tool to construct dynamic laws– Predictive
• Economics (?)