Fluctuation-Response Relation in Non-Equilibrium Systems and Active Matter

TL;DR

This paper derives a general fluctuation-response relation applicable to both equilibrium and non-equilibrium many-body systems, including fluids and active matter, extending the fluctuation-dissipation theorem beyond equilibrium.

Contribution

It introduces a unified relation between correlation and response functions valid in non-equilibrium conditions, expanding the theoretical framework of fluctuation-response relations.

Findings

Derived a general relation valid in equilibrium and non-equilibrium

Applied the relation to fluids in various states

Extended fluctuation-dissipation concepts to 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 non-equilibrium states, when it is not. We illustrate our results by discussing fluids, both in equilibrium and non-equilibrium states, as well as several active-matter systems.