On the second fluctuation--dissipation theorem for nonequilibrium baths

TL;DR

This paper extends the second fluctuation-dissipation theorem to nonequilibrium environments, revealing how active baths modify Langevin dynamics and break the Einstein relation through frenetic contributions.

Contribution

It provides a proper nonequilibrium extension of the fluctuation-dissipation theorem for active environments, deriving the effective Langevin dynamics of a probe.

Findings

Frenetic contributions modify friction in nonequilibrium baths

Standard Einstein relation is broken in active environments

Derived effective Langevin dynamics for probes in nonequilibrium baths

Abstract

Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation-dissipation theorem. We show what is the proper nonequilibrium extension, to be applied when the environment is itself active and driven. In particular we determine the effective Langevin dynamics of a probe from integrating out a steady nonequilibrium environment. The friction kernel picks up a frenetic contribution, i.e., involving the environment's dynamical activity, responsible for the breaking of the standard Einstein relation.