Fluctuation theorems in inhomogenious media under coarse graining

TL;DR

This paper investigates how fluctuation theorems for work and entropy behave in media with spatially varying friction, showing they remain valid but require careful analysis in overdamped systems.

Contribution

It demonstrates that fluctuation relations hold in inhomogeneous media and highlights the importance of proper calculus application in overdamped systems.

Findings

Fluctuation relations are unaffected by spatially varying friction.

Overdamped systems require careful calculus to avoid inconsistencies.

Relations hold in both underdamped and overdamped regimes.

Abstract

We compare the fluctuation relations for work and entropy in underdamped and overdamped systems, when the friction coefficient of the medium is space-dependent. We find that these relations remain unaffected in both cases. However, for the overdamped system, the analysis is more involved, and a blind application of normal rules of calculus would lead to inconsistent results.