A measure of majorisation emerging from single-shot statistical mechanics

TL;DR

This paper introduces a new measure based on majorisation that better predicts the guaranteed work extractable in single-shot thermodynamic processes, challenging the traditional reliance on von Neumann entropy.

Contribution

It proposes a majorisation-based measure as the central quantity in statistical mechanics, especially for non-equilibrium regimes, replacing von Neumann entropy.

Findings

The measure determines the optimal guaranteed work in single-shot scenarios.

In the asymptotic limit, the measure converges to von Neumann entropy.

It governs feasible evolutions via thermal interactions.

Abstract

The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorisation determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy. In the limit of many identical and independent subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered but in the non-equilbrium regime the optimal guaranteed work can be radically different to the optimal average. Moreover our measure of majorisation governs which evolutions can be realized via thermal interactions, whereas the nondecrease of the von Neumann entropy is not sufficiently restrictive. Our results are inspired by single-shot information theory.