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

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.

arXiv comment4 pages, a major revison

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• Far-from-Equilibrium Distribution from Near-Steady-State Work Fluctuations
• Fluctuation Dissipation Relations for Active Field Theories
• Characteristic oscillations in frequency-resolved heat dissipation of linear time-delayed Langevin systems: Approach from the violation of the fluctuation-response relation