Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom

TL;DR

This paper investigates how apparent entropy production in systems with hidden slow degrees of freedom approximately obeys a modified fluctuation theorem, revealing conditions under which hidden properties can be inferred from large deviation analysis.

Contribution

It extends the concept of apparent entropy production to bipartite systems and analyzes the conditions for a modified fluctuation theorem to hold asymptotically.

Findings

Extreme event probabilities follow a modified fluctuation theorem.

Long-term behavior differs from short-time experimental observations.

Hidden properties can be inferred from large deviation functions.

Abstract

The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of freedom that are hidden from the observer, it is not possible to infer the amount of produced entropy exactly. Previous work suggested that a relation similar to the fluctuation theorem may hold at least approximately for such systems if one considers an apparent entropy production. By extending the notion of apparent entropy production to discrete bipartite systems, we investigate which criteria have to be met for such a modified fluctuation theorem to hold in the large deviation limit. We use asymptotic approximations of the large deviation function to show that the probabilities of extreme events of apparent entropy production always obey a modified fluctuation theorem and, moreover, that it is possible to infer otherwise hidden properties. For the paradigmatic case of two coupled colloidal particles on rings the rate function of the apparent entropy production is calculated to illustrate this asymptotic behavior and to show that the modified fluctuation theorem observed experimentally for short observation times does not persist in the long time limit.