Response theory: a trajectory-based approach

TL;DR

This paper reviews recent developments in response theory for nonequilibrium systems, emphasizing trajectory-based methods, symmetry considerations, and the emergence of new phenomena beyond classical fluctuation-dissipation relations.

Contribution

It introduces a trajectory-based response framework for nonequilibrium systems, highlighting the role of frenetic contributions and symmetry considerations, with numerous pedagogical examples.

Findings

Frenetic terms significantly affect responses in nonequilibrium systems.

Modifications to the Sutherland-Einstein relation are discussed.

Negative differential mobilities and response saturation are explained.

Abstract

We collect recent results on deriving useful response relations also for nonequilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation-dissipation relations in equilibrium. For nonequilibrium reference ensembles, the frenetic term contributes essentially and is responsible for new phenomena. We discuss modifications in the Sutherland-Einstein relation, the occurence of negative differential mobilities and the saturation of response. We also indicate how the Einstein relation between noise and friction gets violated for probes coupled to a nonequilibrium environment. We end with some discussion on the situation for quantum phenomena, but the bulk of the text concerns classical mesoscopic (open) systems. The choice of many simple examples is trying to make the notes pedagogical, to introduce an important area of research in nonequilibrium statistical mechanics.