Nonequilibrium fluctuation-response relations for state observables

TL;DR

This paper derives exact fluctuation-response relations for state observables in nonequilibrium Markov processes, providing bounds and insights into fluctuation origins based on system topology.

Contribution

It introduces novel fluctuation-response identities for state observables in nonequilibrium steady states of Markov jump processes, including bounds and topological insights.

Findings

Derived exact fluctuation-response relations for state observables.

Established upper and lower bounds on fluctuations.

Revealed fluctuation properties depend only on system topology.

Abstract

Time-integrated state observables, which quantify the fraction of time spent by the system in a specific pool of states, are important in many fields, such as chemical sensing or the theory of fluorescence spectroscopy. We derive exact identities, called Fluctuation-Response Relations (FRRs), that connect the fluctuations of such observables to their response to external perturbations in nonequilibrium steady state of Markov jump processes. Using these results, we derive a first known upper bound on fluctuations of state observables, as well as some new lower bounds. We further demonstrate how our identities provide a deeper understanding of the mechanistic origin of fluctuations and reveal their properties dependent only on system topology, which may be relevant for model inference using measured data.