Thermodynamic Skewness Relation From Detailed Fluctuation Theorem

TL;DR

This paper derives a fundamental lower bound on the skewness of entropy production distributions from the detailed fluctuation theorem, extending thermodynamic understanding beyond mean and variance, with applications to quantum heat exchange.

Contribution

It establishes a new thermodynamic inequality linking skewness to mean entropy production, revealing non-Gaussian fluctuation constraints far from equilibrium.

Findings

Skewness has a negative lower bound dictated by the DFT.

The bound is validated in a quantum heat exchange model.

Results extend fluctuation theorems to higher-order moments.

Abstract

The detailed fluctuation theorem (DFT) is a statement about the asymmetry in the statistics of the entropy production. Consequences of the DFT are the second law of thermodynamics and the thermodynamics uncertainty relation (TUR), which translate into lower bounds for the mean and variance of currents, respectively. However, far from equilibrium, mean and variance are not enough to characterize the underlying distribution of the entropy production. The fluctuations are not necessarily Gaussian (nor symmetric), which means its skewness could be nonzero. We prove that the DFT imposes a negative tight lower bound for the skewness of the entropy production as a function of the mean. As application, we check the bound in the heat exchange problem between two thermal reservoirs mediated by a qubit swap engine.