Equality connecting energy dissipation with violation of fluctuation-response relation

TL;DR

This paper proves an equality linking energy dissipation rate to the violation of the fluctuation-response relation in non-equilibrium Langevin systems, enabling experimental measurement of dissipation.

Contribution

It establishes a novel equality connecting energy dissipation with FRR violation in non-equilibrium Langevin systems, providing a practical way to measure dissipation.

Findings

Equality between FRR violation and energy dissipation rate proved

Quantification of FRR violation allows experimental estimation of dissipation

Applicable to non-equilibrium Langevin systems

Abstract

In systems driven away from equilibrium, the velocity correlation function and the linear response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems under non-equilibrium conditions. This equality enables us to calculate the rate of energy dissipation by quantifying the extent of the FRR violation, which can be measured experimentally.