Violation of the second fluctuation-dissipation relation and entropy production in nonequilibrium medium

TL;DR

This paper explores how the second fluctuation-dissipation relation is violated in nonequilibrium media described by Langevin dynamics, deriving bounds and analyzing effective dynamics with an example involving stochastically switching potentials.

Contribution

It derives an inequality bounding the violation of the second FDR in nonequilibrium media and compares effective dynamics from different theoretical approaches.

Findings

Second FDR violation bounds derived for nonequilibrium media

Effective dynamics are consistent across linear response and perturbation methods

Second FDR is recovered in the fast switching limit despite nonequilibrium conditions

Abstract

We investigate a class of nonequilibrium media described by Langevin dynamics that satisfies the local detailed balance. For the effective dynamics of a probe immersed in the medium, we derive an inequality that bounds the violation of the second fluctuation-dissipation relation (FDR). We also discuss the validity of the effective dynamics. In particular, we show that the effective dynamics obtained from nonequilibrium linear response theory is consistent with that obtained from a singular perturbation method. As an example of these results, we propose a simple model for a nonequilibrium medium in which the particles are subjected to potentials that switch stochastically. For this model, we show that the second FDR is recovered in the fast switching limit, although the particles are out of equilibrium.