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Time reversal in nonequilibrium thermodynamics.

Michal Pavelka1, Václav Klika2, Miroslav Grmela3

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The general equation of nonequilibrium reversible-irreversible coupling (GENERIC) generalizes Onsager-Casimir reciprocal relations beyond near-equilibrium conditions. This study reveals a new structure for these relations, applicable even far from equilibrium.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • The general equation of nonequilibrium reversible-irreversible coupling (GENERIC) is a fundamental framework for describing thermodynamic systems.
  • Onsager-Casimir reciprocal relations are crucial for understanding transport phenomena near equilibrium.

Purpose of the Study:

  • To investigate the implications of the GENERIC framework concerning time-reversal transformations.
  • To generalize Onsager-Casimir reciprocal relations to systems far from thermodynamic equilibrium.

Main Methods:

  • Analysis of the GENERIC framework under time-reversal transformations.
  • Identification of a generalized structure for reciprocal relations.
  • Application and illustration across various physical systems.

Main Results:

  • Onsager-Casimir reciprocal relations are shown to be implied by GENERIC in the near-equilibrium regime.
  • A general structure enabling reciprocal relations valid far from equilibrium is identified.
  • The study provides a generalized form of Onsager-Casimir reciprocal relations for non-equilibrium systems.

Conclusions:

  • The GENERIC framework provides a unified approach to reciprocal relations in both near- and far-from-equilibrium regimes.
  • The identified structure offers a powerful tool for analyzing irreversible processes.
  • The findings are illustrated in diverse areas including Hamiltonian dynamics and quantum mechanics.