Upper bound for the average entropy production based on stochastic entropy extrema

TL;DR

This paper derives an upper bound for the average entropy production in stochastic thermodynamics using extrema of stochastic trajectories, linking it to the supremum of entropy production in non-equilibrium systems.

Contribution

It introduces a new inequality to bound average entropy production based on stochastic entropy extrema, extending fluctuation relation analysis.

Findings

Upper bounds of average entropy production are established.

The average total entropy production is bounded by its supremum.

Results apply to general non-equilibrium stationary systems.

Abstract

The second law of thermodynamics, which asserts the non-negativity of the average total entropy production of a combined system and its environment, is a direct consequence of applying Jensen's inequality to a fluctuation relation. It is also possible, through this inequality, to determine an upper bound of the average total entropy production based on the entropies along the most extreme stochastic trajectories. In this work, we construct an upper bound inequality of the average of a convex function over a domain whose average is known. When applied to the various fluctuation relations, the upper bounds of the average total entropy production are established. Finally, by employing the result of Neri, Rold\'an, and J\"ulicher [Phys. Rev. X 7, 011019 (2017)], we are able to show that the average total entropy production is bounded only by the total entropy production supremum, and vice versa, for a general non-equilibrium stationary system.