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Non - equilibrium thermodynamics B eyond local equilibrium and local state

Weakly nonlocal non - equilibrium thermodynamics Peter Ván Budapest University of Technology and Economics, Department of Chemical Physics. Non - equilibrium thermodynamics B eyond local equilibrium and local state Exploitations of the Second Law - Liu procedure Examples

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Non - equilibrium thermodynamics B eyond local equilibrium and local state

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  1. Weakly nonlocal non-equilibrium thermodynamicsPeter VánBudapest University of Technology and Economics, Department of Chemical Physics • Non-equilibrium thermodynamics • Beyond local equilibrium and local state • Exploitations of the Second Law - Liu procedure • Examples • Guyer-Krumhansl equation • Ginzburg-Landau equation • One component fluid mechanics - quantum (?) fluids • Conclusions

  2. Classical Irreversible Thermodynamics Local equilibrium (~ there is no microstructure) • Beyond local equilibrium(nonlocality): • in time (memory effects) • in space (structure effects) dynamic variables ? Method: local state and beyond …

  3. Nonlocalities: Restrictions from the Second Law.

  4. weakly nonlocal Non-equilibrium thermodynamics basic balances (and more) • basic state: • constitutive state: • constitutive functions: Second law: (universality) Constitutive theory Method: Liu procedure Speciality: constructive

  5. Weakly nonlocalextended thermodynamics state space constitutive functions local state: Liu procedure (Farkas’s lemma): solution?

  6. extended (Gyarmati) entropy entropy current (Nyíri) (B – current multiplier) local? balance?

  7. Weakly nonlocal internal variables Ginzburg-Landau (variational): • Second Law • Variational (!)

  8. Ginzburg-Landau (thermodynamic, relocalized) state space constitutive functions local state Liu procedure (Farkas’s lemma) ?

  9. current multiplier isotropy

  10. Ginzburg-Landau (thermodynamic, non relocalizable) state space constitutive functions Liu procedure (Farkas’s lemma)

  11. One component weakly nonlocal fluids and quantum mechanics

  12. Schrödinger equation: Madelung transformation: de Broglie-Bohm form: Hydrodynamic form:

  13. One component weakly nonlocal fluid basic state constitutive state constitutive functions Liu procedure (Farkas’s lemma):

  14. (Fisher entropy) reversible pressure Schrödinger-Madelung fluid

  15. Schrödinger equation: Madelung transformation: de Broglie-Bohm form: Hydrodynamic form:

  16. One component weakly nonlocal fluid basic state constitutive state constitutive functions Liu procedure (Farkas’s lemma):

  17. (Fisher entropy) reversible pressure Schrödinger-Madelung fluid

  18. Potential form: Bernoulli equation Schrödinger equation Euler-Lagrange form Variational origin

  19. Why nonequilibrium thermodynamics? science of temperature Thermodynamics science of macroscopic energy changes Thermodynamics • general framework of any • Thermodynamics (?) macroscopic (?) • continuum (?) • theories • General framework: • fundamental balances • objectivity - frame indifference • Second Law reversibility – special limit

  20. Conclusions • Not everything is a balance • Second order nonlocality is interesting • Constitutive entropy current • Force-current systems: constructivity • Variational principles Second Law

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