An update on nonequilibrium linear response

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.

v2: removed typos, updated refs

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• Interacting Brownian dynamics in a nonequilibrium particle bath
• Nonequilibrium fluctuation-dissipation theorem and heat production
• Energetics of active fluctuations in living cells
• Limits of Predictions in Thermodynamic Systems: A Review
• Anomalous force-velocity relation of driven inertial tracers in steady laminar flows
• Thermal response of nonequilibrium RC-circuits
• Thermal response in driven diffusive systems
• Negative response to an excessive bias by a mixed population of voters