Fluctuation-Dissipation relations far from Equilibrium

TL;DR

This paper reviews recent advances in non-equilibrium linear response theory, focusing on generalized fluctuation-dissipation relations for Markov processes, aging systems, and phase-ordering dynamics, highlighting how static and dynamic properties are interconnected or can be decoupled.

Contribution

It presents a comprehensive review of generalized fluctuation-dissipation theorems for non-equilibrium systems, including aging and phase-ordering, and discusses conditions under which static-dynamic relations hold or break down.

Findings

Generalized fluctuation-dissipation relations are derived for Markov processes.

Scaling properties of linear response functions depend on topological defects.

Connections between statics and dynamics can be violated at lower critical dimensions.

Abstract

In this Article we review some recent progresses in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation-dissipation theorem can be derived for Markov processes, and discuss the Cugliandolo-Kurchan \cite{Cugliandolo93} fluctuation dissipation relation for aging systems and the theorem by Franz {\it et. al.} \cite{Franz98} relating static and dynamic properties. We than specialize the subject to phase-ordering systems examining the scaling properties of the linear response function and how these are determined by the behavior of topological defects. We discuss how the connection between statics and dynamics can be violated in these systems at the lower critical dimension or as due to stochastic instability.