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 (20)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Stochastic thermodynamics: Principles and perspectives
• Statistical Physics of Self-Replication
• Universality of efficiency at maximum power
• Stochastic thermodynamics under coarse-graining
• Fluctuation theorems for stochastic dynamics
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Stochastic thermodynamics of chemical reaction networks
• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Stochastic Lattice Gas Model for a Predator-Prey System
• 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
• Entropy production in full phase space for continuous stochastic dynamics
• Entropy production in the majority-vote model
• A possible classification of nonequilibrium steady states
• Generalized Clausius relation and power dissipation in non equilibrium stochastic systems
• Fourier's law from a chain of coupled planar harmonic oscillators under energy conserving noise
• Reversibility, heat dissipation and the importance of the thermal environment in stochastic models of nonequilibrium steady states
• Dynamics of the directed Ising chain
• Stochastic Thermodynamics Across Scales: Emergent Inter-attractoral Discrete Markov Jump Process and Its Underlying Continuous Diffusion
• Entropy production in continuous phase space systems

Cited by in corpus (36)

• Power-efficiency-dissipation relations in linear thermodynamics
• Onsager coefficients in periodically driven systems
• Analytic approaches of the anomalous diffusion: a review
• Entropy production as tool for characterizing nonequilibrium phase transitions
• Quantum Fokker-Planck-Kramers equation and entropy production
• Maximal power for heat engines: role of asymmetric interaction times
• Stochastic thermodynamics for a periodically driven single-particle pump
• Stochastic thermodynamics and entropy production of chemical reaction systems
• Thermodynamics of collisional models for Brownian particles: General properties and efficiency
• Current fluctuations in nonequilibrium discontinuous phase transitions
• Nonequilibrium thermodynamic potentials for continuous-time Markov chains
• Entropy production and heat capacity of systems under time-dependent oscillating temperature
• Stochastic thermodynamics of opinion dynamics
• Linear response in large deviations theory: A method to compute non-equilibrium distributions
• Hyperaccurate bounds in discrete-state Markovian systems
• General linear thermodynamics for periodically driven systems with multiple reservoirs
• Entropy production and heat transport in harmonic chains under time dependent periodic drivings
• The derivation of Markov processes that violate detailed balance
• Entropy production and entropy extraction rates for a Brownian particle that walks in underdamped medium
• Memory and irreversibility on two-dimensional overdamped Brownian dynamics
• Stochastic thermodynamics for kinetic equations
• On entropy production in nonequilibrium systems
• Complex heat capacity and entropy production of temperature modulated systems
• Analysis of the earlier times and flux of the entropy on the majority voter model with difusion
• Maxwell's demon and the management of ignorance in stochastic thermodynamics
• Boltzmann stochastic thermodynamics
• Obtaining efficient collisional engines via velocity dependent drivings
• 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
• How Geometrical Frustrated Systems Challenge our Notion of Thermodynamics
• Effect of viscous friction on entropy, entropy production and entropy extraction rates in underdamped and overdamped media
• Information entropy and temperature of the binary Markov chains
• Explicit noise and dissipation operators for quantum stochastic thermodynamics
• Rotational diffusion under torque: Microscopic reversibility and excess entropy
• Positive heat capacity in the microcanonical ensemble