An expression for stationary distribution in nonequilibrium steady state

TL;DR

This paper derives an approximate expression for the stationary distribution of nonequilibrium steady states in stochastic systems, linking it to excess entropy changes and conditioned heat transfer, with potential experimental verification.

Contribution

The authors provide a second-order accurate formula for the stationary distribution in nonequilibrium systems based on fluctuation theorems, connecting it to excess entropy and heat transfer.

Findings

Derived concise expression for stationary distribution

Expressed probability in terms of excess entropy change

Potential for experimental verification in mesoscopic systems

Abstract

We study the nonequilibrium steady state realized in a general stochastic system attached to multiple heat baths and/or driven by an external force. Starting from the detailed fluctuation theorem we derive concise and suggestive expressions for the corresponding stationary distribution which are correct up to the second order in thermodynamic forces. The probability of a microstate $\eta$ is proportional to $\exp[{\Phi}(\eta)]$ where ${\Phi}(\eta)=-\sum_k\beta_k\mathcal{E}_k(\eta)$ is the excess entropy change. Here $\mathcal{E}_k(\eta)$ is the difference between two kinds of conditioned path ensemble averages of excess heat transfer from the $k$-th heat bath whose inverse temperature is $\beta_k$. Our expression may be verified experimentally in nonequilibrium states realized, for example, in mesoscopic systems.