Modified Jarzynski Relation for non-Markovian noise

TL;DR

This paper shows that the standard Jarzynski relation is violated in non-Markovian systems with colored noise, providing an exact correction formula depending on the noise's autocorrelation time, and identifies conditions where the relation still holds.

Contribution

The authors derive a modified Jarzynski relation accounting for non-Markovian colored noise, extending the applicability of fluctuation theorems to such systems.

Findings

Conventional Jarzynski relation is violated by non-Markovian colored noise.

Derived an exact expression for dissipative energy involving noise autocorrelation.

In Gaussian and slow processes, the standard Jarzynski relation is recovered.

Abstract

We demonstrate the conventional Jarzynski relation (JR) is violated for a non-Markovian process with colored noise. As an example an exactly soluble model is considered with a simple protocol for the external work performed on the system along a non-equilibrium trajectory. For that model we derive an exact expression for the dissipative energy in terms of an arbitrary correlator of the noise characterized by an autocorrelation time $t_c$. As the result we find corrections to the JR in terms of $t_c$. In the limiting case of a Gaussian process as well as an infinitely slow process the conventional JR is retained. The result is valid for an arbitrary colored noise.