The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of...
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Transcript of The meaning of the Second Law: Nonlocal effects in continuum physics Peter Ván BUTE, Department of...
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
– ConceptsConcepts and theories– What kind of thermodynamics?
Discrete(homogeneous)
T(t)
ContinuumT(t,x)
Phenomenological(T is primitive)
Statistical(T is explained)
Equilibrium Irreversible
Second Law
– time dependence – time reversal – variational principles – S exists– S is increasing – local equilibrium
Can be interpreted in a thermodynamic theory
Irreversibility
(?)
(?)
(?)
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
1 + 2 + closed system
S is a Ljapunov function of the equilibrium of the dynamic law
Irreversibility trend to equilibrium
Classical Irreversible
Thermodynamics
Local equilibrium (= there is no microstructure)
Violations (nonlocality):
•in time (memory effects)•in space (structure effects)
dynamic variables?
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
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
Conclusions
– Second Law is a stability criteria (Irreversibility is a kind of stability)
– Second Law is a tool to construct dynamic laws– Predictive
• Economics (?)