Fluctuation-response relation in nonequilibrium systems and active matter.

Abstract

We use dynamic equations to derive a relation between correlation functions and response or relaxation functions in many-body systems. The relation is very general and holds both in equilibrium, when the usual fluctuation-dissipation theorem is valid, and to linear order in an expansion about arbitrary nonequilibrium states, when it is not. It provides a simple way to observe microscopic correlations via a system's macroscopic response, even in situations where the correlations are difficult to observe directly, and the response is not determined by the standard commutator (i.e., antisymmetrized) correlation functions. We illustrate our results by discussing fluids, both in equilibrium and nonequilibrium states, as well as several active-matter systems.