Fluctuation-dissipation theorem in nonequilibrium steady states

¹  II. Institut für Theoretische Physik, Universität Stuttgart - 70550 Stuttgart, Germany, EU
²  Department of Chemistry, University of California - Berkeley, CA 94720, USA
³  Chemical Sciences Division, Lawrence Berkeley National Laboratory - Berkeley, CA 94720, USA

Received: 31 July 2009
Accepted: 9 December 2009

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 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 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 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 a priori surprising freedom apparently involved in different forms of the FDT in a NESS is clarified.