Fluctuation-Dissipation Relations in Active Matter Systems

TL;DR

This paper derives a compact fluctuation-dissipation relation for active matter, specifically AOUP models, revealing how non-equilibrium behavior can be characterized through correlations and the influence of dimensionality.

Contribution

It introduces a new, explicit fluctuation-dissipation relation for active Ornstein-Uhlenbeck particles that separates equilibrium and non-equilibrium effects, enhancing understanding of active matter dynamics.

Findings

FDR explicitly separates equilibrium and non-equilibrium contributions.

Dimensionality affects the relaxation dynamics in AOUP systems.

Information about the distance from equilibrium can be inferred from the FDR.

Abstract

We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein-Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation-dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one, two, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.