Moment generating function bound from detailed fluctuation theorem

TL;DR

This paper derives a lower bound on the moment generating function of entropy production from the detailed fluctuation theorem, providing insights into fluctuation behavior in thermodynamic systems.

Contribution

It introduces a novel lower bound on the MGF of entropy production based on the detailed FT, extending understanding of fluctuation properties beyond the second law.

Findings

Bound verified for heat exchange between reservoirs

Bound satisfied in qubit swap engine

Provides a new tool for analyzing entropy fluctuations

Abstract

A famous consequence of the detailed fluctuation theorem (FT), $p(\Sigma)/p(-\Sigma)=\exp{(\Sigma)}$, is the integral FT $\langle \exp(-\Sigma)\rangle =1$ for a random variable $\Sigma$ and a distribution $p(\Sigma)$. When $\Sigma$ represents the entropy production in thermodynamics, the main outcome of the integral FT is the second law, $\langle \Sigma \rangle \geq 0$. However, a full description of the fluctuations of $\Sigma$ might require knowledge of the moment generating function (MGF), $G(\alpha):=\langle \exp(\alpha \Sigma) \rangle$. In the context of the detailed FT, we show the MGF is lower bounded in the form $G(\alpha)\geq B(\alpha,\langle\Sigma\rangle)$ for a given mean $\langle\Sigma\rangle$. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a weakly coupled bosonic mode and a qubit swap engine.