Fluctuation-response relation of time-symmetric quantities around general nonequilibrium stationary state

TL;DR

This paper establishes a novel fluctuation-response relation for time-symmetric quantities in general nonequilibrium stationary states, using a decomposition method to connect fluctuations with responses.

Contribution

It introduces a new fluctuation-response relation for time-symmetric observables in nonequilibrium states via a fictitious stalling decomposition technique.

Findings

Fluctuations of empirical measures relate to responses of measures and currents.

The decomposition method applies to general nonequilibrium stationary states.

The relation is proven using a stalling state decomposition approach.

Abstract

A connection between the response and fluctuation in general nonequilibrium stationary states is investigated. We focus on time-symmetric quantities and find that the fluctuation of a kind of empirical measure can be expressed with the response of the empirical measure, current, and the time-symmetric current. This relation is proven by using the fictitious stalling decomposition: We decompose a single observed transition (edge in the state space) between two microscopic states into two transitions such that one of the transitions stalls in this stationary state. Through this trick, relations for stalling stationary states apply to general nonequilibrium stationary states, which leads to the desired relation.