Hidden slow degrees of freedom and fluctuation theorems: an analytically solvable model

TL;DR

This paper introduces an analytically solvable model in stochastic thermodynamics demonstrating how hidden slow degrees of freedom affect fluctuation theorems, and proposes a marginal entropy production that restores the theorems' validity.

Contribution

It provides a solvable model illustrating the impact of hidden degrees of freedom on fluctuation theorems and introduces a new entropy measure that satisfies the theorems.

Findings

Apparent entropy production violates standard fluctuation theorems due to hidden degrees of freedom.

The marginal entropy production restores the fluctuation theorems in the presence of hidden slow variables.

Non-Markovianity of the visible process causes deviations from the standard fluctuation theorems.

Abstract

In some situations in stochastic thermodynamics not all relevant slow degrees of freedom are accessible. Consequently, one adopts an effective description involving only the visible degrees of freedom. This gives rise to an apparent entropy production that violates standard fluctuation theorems. We present an analytically solvable model illustrating how the fluctuation theorems are modified. Furthermore, we define an alternative to the apparent entropy production: the marginal entropy production which fulfills the fluctuation theorems in the usual form. We show that the non-Markovianity of the visible process is responsible for the deviations in the fluctuation theorems.