Macroscopic Expression Connecting the Rate of Energy Dissipation and Violation of the Fluctuation-Response Relation

TL;DR

This paper establishes a direct quantitative link between the violation of the fluctuation-response relation and the energy dissipation rate in nonequilibrium systems, specifically in colloidal suspensions.

Contribution

It introduces a field-variable-based equality connecting FRR violation magnitude to energy dissipation rate in nonequilibrium systems.

Findings

FRR violation magnitude relates to energy dissipation rate.

The equality applies to scalar and vector potentials of velocity fields.

Violation of FRR captures the entropic component of dissipated free energy.

Abstract

A direct connection between the magnitude of the violation of the fluctuation-response relation (FRR) and the rate of energy dissipation is presented in terms of field variables of nonequilibrium systems. Here, we consider the density field of a colloidal suspension either in a relaxation process or in a nonequilibrium steady state driven by an external field. Using a path-integral representation of the temporal evolution of the density field, we find an equality that relates the magnitude of the violation of the FRR for scalar and vector potentials of the velocity field to the rate of energy dissipation for the entire system. Our result demonstrates that the violation of the FRR for field variables captures the entropic component of the dissipated free energy.