The Statistical Foundation of Entropy in Extended Irreversible Thermodynamics

Abstract

In the theory of extended irreversible thermodynamics (EIT), the flux-dependent entropy function plays a key role and has a fundamental distinction from the usual flux-independent entropy function adopted by classical irreversible thermodynamics (CIT). However, its existence, as a prerequisite for EIT, and its statistical origin have never been justified. In this work, by studying the macroscopic limit of an ε-dependent Langevin dynamics, which admits a large deviations (LD) principle, we show that the stationary LD rate functions of probability density p_ε(x; t) and joint probability density p_ε(x; \dot{x}; t) actually turn out to be the desired fluxindependent entropy function in CIT and flux-dependent entropy function in EIT respectively. The difference of the two entropy functions is determined by the time resolution for Brownian motions times a Lagrangian, the latter arises from the LD Hamilton-Jacobi equation and can be used for constructing conserved Lagrangian/Hamiltonian dynamics.

arXiv comment22 pages, 1 figure

References in corpus (22)

• The large deviation approach to statistical mechanics
• Dynamical ensembles in stationary states
• Steady State Thermodynamics of Langevin Systems
• Stochastic thermodynamics: Principles and perspectives
• Three detailed fluctuation theorems
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Nonequilibrium Physics in Biology
• Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
• The Physical Origins of Entropy Production, Free Energy Dissipation and their Mathematical Representations
• Mesoscopic Kinetic Basis of Macroscopic Chemical Thermodynamics: A Mathematical Theory
• Entropy Production in Mesoscopic Stochastic Thermodynamics: Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures, and Mechanical Forces
• Level 2 large deviation functionals for systems with and without detailed balance
• Dissipation, Generalized Free Energy, and a Self-consistent Nonequilibrium Thermodynamics of Chemically Driven Open Subsystems
• Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear Chemical Reaction Systems with General Rate Law
• Inertial Effects in Non-Equilibrium Thermodynamics
• The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
• Analytical Mechanics in Stochastic Dynamics: Most Probable Path, Large-Deviation Rate Function and Hamilton-Jacobi Equation
• Stochastic thermodynamics with odd controlling parameters
• Kinematic Basis of Emergent Energetics of Complex Dynamics
• Nonlinear Stochastic Dynamics of Complex Systems, I: A Chemical Reaction Kinetic Perspective with Mesoscopic Nonequilibrium Thermodynamics
• Stochastic Dynamics II: Finite Random Dynamical Systems, Linear Representation, and Entropy Production
• Macroscopic fluxes and local reciprocal relation in second-order stochastic processes far from equilibrium

Cited by in corpus (3)

• Dynamical mean-field theory: from ecosystems to reaction networks
• Stochastic Dynamics, Large Deviations Principle, and Non-equilibrium Thermodynamics
• Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes