Exact equalities and thermodynamic relations for nonequilibrium steady states

TL;DR

This paper establishes exact thermodynamic equalities and relations for nonequilibrium steady states using Markov jump processes, including a NESS version of the Jarzynski equality and an extended Clausius relation, with rigorous proofs.

Contribution

It introduces a rigorous framework for thermodynamics of NESS, deriving new equalities and a microscopic entropy representation.

Findings

Proves a NESS version of the Jarzynski equality.

Derives an extended Clausius relation for NESS.

Provides a microscopic representation of nonequilibrium entropy.

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.