A Jarzynski-type equality for nonequilibrium steady-state probabilities

TL;DR

This paper introduces a Jarzynski-like equality for nonequilibrium steady-state probabilities, enabling their reconstruction from weighted finite-time loop-erased paths, and reveals underlying thermodynamic symmetries.

Contribution

It presents a novel Jarzynski-type equality for nonequilibrium steady states and links path probabilities to thermodynamic quantities.

Findings

Reconstruction of steady-state probabilities from path averages.

Derivation of a Jarzynski-type equality for nonequilibrium systems.

Identification of thermodynamic symmetry relations for path probabilities.

Abstract

We show that steady-state probabilities of a nonequilibrium Markovian system can be reconstructed from a weighted ensemble average of finite-time loop-erased paths. Each path $\Gamma$ is weighted by $e^{-S(\Gamma)}$, where $S(\Gamma)$ can be interpreted either as the action functional or as the entropy change in the surrounding reservoirs. In doing so, we uncover a Jarzynski-type equality for nonequilibrium steady states. We also reveal that the probabilities of loop-erased paths obey strong thermodynamic symmetry relations.