Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions

TL;DR

This paper derives a general linear response formula for nonequilibrium Markov jump processes and overdamped diffusions, expressing responses in terms of correlation functions involving entropy flux and dynamical activity, applicable without detailed distribution knowledge.

Contribution

It introduces a unified response formula for nonequilibrium systems based on correlation functions, extending linear response theory beyond equilibrium conditions.

Findings

Response formula involves entropy flux and dynamical activity correlations.

Applicable to all observables without needing the nonequilibrium distribution.

Provides a basis for numerical and experimental evaluation of responses.

Abstract

Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.