Nonequilibrium thermodynamic potentials for continuous-time Markov chains

TL;DR

This paper introduces nonequilibrium thermodynamic potentials for continuous-time Markov chains by linking equilibrium fluctuations to nonequilibrium stationary processes, providing a variational framework and generalized relations.

Contribution

It develops a novel theoretical framework for NE thermodynamic potentials, including dual ensembles and Legendre duality, for continuous-time Markov chains.

Findings

NE potentials are Legendre duals of equilibrium fluctuations.

A variational principle characterizes NE potentials and states.

Generalized NE Maxwell relations extend Onsager reciprocity.

Abstract

We connect the rare fluctuations of an Equilibrium (EQ) process and the typical fluctuations of a nonequilibrium (NE) stationary process. In the framework of large deviation theory, this observation allows us to introduce NE thermodynamic potentials. For continuous-time Markov chains, we identify the relevant pairs of conjugated variables and propose two NE ensembles: one with fixed dynamics and fluctuating time-averaged variables, and another with fixed time-averaged variables, but a fluctuating dynamics. Accordingly, we show that NE processes are equivalent to conditioned EQ processes ensuring that NE potentials are Legendre dual. We find a variational principle satisfied by the NE potentials that reach their maximum in the NE stationary state and whose first derivatives produce the NE equations of state, and second derivatives produce the NE Maxwell relations generalizing the Onsager reciprocity relations.