Fluctuation-Dissipation Theorem in Nonequilibrium Steady States

TL;DR

This paper extends the fluctuation-dissipation theorem to nonequilibrium steady states, linking response functions to entropy-related correlations and clarifying the differences from equilibrium cases.

Contribution

It introduces a generalized FDT for NESS involving entropy conjugate variables and clarifies the role of total entropy production in the theorem.

Findings

FDT in NESS involves entropy conjugate variables.

Difference from equilibrium FDT is an additive entropy term.

A variant of FDT useful for coupled Langevin systems.

Abstract

In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the response of an observable to a small perturbation by a correlation function of this variable with another one that is conjugate to the perturbation with respect to \emph{energy}. For a nonequilibrium steady state (NESS), the corresponding FDT is shown to involve in the correlation function a variable that is conjugate with respect to \emph{entropy}. By splitting up entropy production into one of the system and one of the medium, it is shown that for systems with a genuine equilibrium state the FDT of the NESS differs from its equilibrium form by an additive term involving \emph{total} entropy production. A related variant of the FDT not requiring explicit knowledge of the stationary state is particularly useful for coupled Langevin systems. The \emph{a priori} surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.