Fluctuation-response inequality out of equilibrium

TL;DR

This paper introduces a fluctuation-response inequality (FRI) that bounds the response of out-of-equilibrium systems using fluctuations and information-theoretic measures, linking response theory with thermodynamics and information theory.

Contribution

The paper develops a new fluctuation-response inequality applicable to arbitrary out-of-equilibrium states, connecting response bounds with information theory and extending thermodynamic uncertainty relations.

Findings

Response magnitude is bounded by fluctuations and Kullback-Leibler divergence.

Differential mobility is bounded by diffusivity in steady states.

Generalized uncertainty relation involving higher-order cumulants is derived.

Abstract

We present a new approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady state particle transport, the differential mobility is bounded by the diffusivity. For a virtual perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.