Dynamical Fluctuation-Response Relations

TL;DR

This paper derives exact dynamical fluctuation-response relations for nonautonomous Markov jump processes, enhancing understanding of response inequalities and unifying various fluctuation relations.

Contribution

It provides a unified framework for dynamical FRRs, sharpening existing thermodynamic and kinetic uncertainty relations, and recovering classical fluctuation-dissipation results.

Findings

Derivation of exact finite-time covariance relations.

Sharpening of fluctuation-response inequalities.

Recovery of classical fluctuation-dissipation theorem and Onsager reciprocity.

Abstract

We derive exact dynamical fluctuation-response relations (FRRs) for time-integrated observables of any nonautonomous Markov jump process. The finite-time covariance splits into an initial variability and an integral of response kernels along the driven dynamics. The identity sharpens the dynamical response thermodynamic and kinetic uncertainty relations and fluctuation-response inequalities (FRIs). It also recovers steady-state FRRs, fluctuation-dissipation theorem and Onsager reciprocity, identifies known autonomous FRIs as the zero-frequency mode.