An update on nonequilibrium linear response

TL;DR

This paper reviews and compares different linear response formulas for nonequilibrium systems, highlighting a dynamical systems approach that remains valid without smooth stationary distributions, and discusses implications for physical understanding.

Contribution

It demonstrates the effectiveness of a dynamical systems-based linear response formula for stochastic dynamics and explores new physical insights from probabilistic approaches.

Findings

Dynamical systems approach works for stochastic dynamics.

Numerical example on circadian cycles perturbation.

Discussion of frenetic contributions and dynamical activity.

Abstract

The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance, introduces the logarithm of the stationary probability density as observable. The theory of dynamical systems offers an alternative with a formula that continues to work when the stationary distribution is not smooth. We show that this method works equally well for stochastic dynamics, and we illustrate it with a numerical example for the perturbation of circadian cycles. A second "probabilistic" approach starts from dynamical ensembles and expands the probability weights on path space. This line suggests new physical questions, as we meet the frenetic contribution to linear response, and the relevance of the change in dynamical activity in the relaxation to a (new) nonequilibrium condition.