Fluctuation relations and coarse-graining

TL;DR

This paper investigates how fluctuation relations apply to coarse-grained stochastic systems, showing that approximate relations hold and deviations may stem from unobserved variables, with implications for experimental observations.

Contribution

It introduces a perturbative method to derive approximate fluctuation relations for coarse-grained Markovian jump processes, highlighting the effect of unobserved degrees of freedom.

Findings

Approximate fluctuation relations are valid for coarse-grained dynamics.

Deviations from fluctuation relations can be caused by unobserved degrees of freedom.

Large deviation analysis illustrates the impact of coarse-graining on fluctuation behavior.

Abstract

We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian jump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.