Exact equalities and thermodynamic relations for nonequilibrium steady states

Abstract

We study thermodynamic operations which bring a nonequilibrium steady state (NESS) to another NESS in physical systems under nonequilibrium conditions. We model the system by a suitable Markov jump process, and treat thermodynamic operations as protocols according to which the external agent varies parameters of the Markov process. Then we prove, among other relations, a NESS version of the Jarzynski equality and the extended Clausius relation. The latter can be a starting point of thermodynamics for NESS. We also find that the corresponding nonequilibrium entropy has a microscopic representation in terms of symmetrized Shannon entropy in systems where the microscopic description of states involves "momenta". All the results in the present paper are mathematically rigorous.

58 pages, 8 figures; many small improvements have been made in version 2

References in corpus (11)

• Fluctuations and response of nonequilibrium states
• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• An expression for stationary distribution in nonequilibrium steady state
• The frenetic origin of negative differential response
• Representation of nonequilibrium steady states in large mechanical systems
• Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process
• Possible extended forms of thermodynamic entropy
• Inconsistencies in steady state thermodynamics
• Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem
• Nonequilibrium heat capacity
• Universal expression for adiabatic pumping in terms of non-equilibrium steady states

Cited by in corpus (18)

• A mechanical autonomous stochastic heat engine
• Nonequilibrium Thermodynamic Formalism of Nonlinear Chemical Reaction Systems with Waage-Guldberg's Law of Mass Action
• Limits of Predictions in Thermodynamic Systems: A Review
• Revisiting the Glansdorff-Prigogine criterion for stability within irreversible thermodynamics
• A general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments
• Zeroth law of thermodynamics for nonequilibrium steady states in contact
• Statistical forces from close--to--equilibrium media
• Large deviations and chemical potential in bulk-driven systems in contact
• Dynamical relaxation behaviors of a critical quench
• Thermal response of nonequilibrium RC-circuits
• Temperature response in nonequilibrium stochastic systems
• Excess entropy production in quantum system: Quantum master equation approach
• Nonequilibrium corrections to gradient flow
• Work, work fluctuations, and the work distribution in a thermal non-equilibrium steady state
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Asymptotic expansion of the solution of the master equation and its application to the speed limit
• Nonequilibrium grand-canonical ensemble built from a physical particle reservoir
• Theory of Applying Heat Flow from Thermostatted Boundary Walls: Dissipative and Local-Equilibrium Responses and Fluctuation Theorems