Nonequilibrium fluctuation-response relations for state-current correlations

TL;DR

This paper extends fluctuation-response relations to include mixed state-current covariances in nonequilibrium Markov processes, revealing how symmetry breaking relates to correlations and demonstrating practical applications in quantum and biological systems.

Contribution

It derives new fluctuation-response relations for mixed covariances and inverse relations for responses, advancing understanding of nonequilibrium correlations and symmetry breaking.

Findings

Breaking Onsager symmetry requires state-current correlations.

FRRs can explain fluctuation behavior in quantum dots.

Applications demonstrated in enzymatic reactions.

Abstract

Recently, novel exact identities known as Fluctuation-Response Relations (FRRs) have been derived for nonequilibrium steady states of Markov jump processes. These identities link the fluctuations of state or current observables to a combination of responses of these observables to perturbations of transition rates. Here, we complement these results by deriving analogous FRRs applicable to mixed covariances of one state and one current observable. We further derive novel Inverse FRRs expressing individual state or current response in terms of a combination of covariances rather than vice versa. Using these relations, we demonstrate that the breaking of the Onsager symmetry requires the presence of state-current correlations. On the practical side, we demonstrate the applicability of FRRs for explaining the behavior of fluctuations in quantum dot devices or enzymatic reaction networks.