Stochastic approach to equilibrium and nonequilibrium thermodynamics

Abstract

We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second, the definition of entropy production rate which is nonnegative and vanishes in thermodynamic equilibrium. Based on these assumptions we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium, and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasi-equilibrium processes, the convexity of the equilibrium surface, the monotonic time behavior of thermodynamic potentials, including entropy, the bilinear form of the entropy production rate, the Onsager coefficients and reciprocal relations, and the nonequilibrium steady states of chemical reactions.

References in corpus (6)

• Fluctuation theorems for stochastic dynamics
• Stochastic thermodynamics of chemical reaction networks
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
• A possible classification of nonequilibrium steady states
• Reversibility, heat dissipation and the importance of the thermal environment in stochastic models of nonequilibrium steady states

Cited by in corpus (14)

• Analytic approaches of the anomalous diffusion: a review
• Quantum Fokker-Planck-Kramers equation and entropy production
• Stochastic thermodynamics for a periodically driven single-particle pump
• Thermodynamics of collisional models for Brownian particles: General properties and efficiency
• Entropy production and heat capacity of systems under time-dependent oscillating temperature
• Linear response in large deviations theory: A method to compute non-equilibrium distributions
• Entropy production and heat transport in harmonic chains under time dependent periodic drivings
• Entropy production and entropy extraction rates for a Brownian particle that walks in underdamped medium
• Analysis of the earlier times and flux of the entropy on the majority voter model with difusion
• Boltzmann stochastic thermodynamics
• Free energy for non-equilibrium quasi-stationary states
• Exact time-dependent analytical solutions for entropy production rate for a system that operates in a heat bath where its temperature varies linearly in space
• Stochastic motion in phase space on a surface of constant energy
• Positive heat capacity in the microcanonical ensemble