Introducing one-shot work into fluctuation relations

TL;DR

This paper explores the connection between fluctuation relations and one-shot statistical mechanics in quantum thermodynamics, establishing bounds that link the two frameworks and enabling experimental testing of one-shot work quantities.

Contribution

It demonstrates how one-shot work quantities can be defined and bounded within the context of fluctuation relations, creating a new bridge between the two approaches.

Findings

Unified notions of work and probability distributions in both frameworks

Derived bounds for one-shot work in fluctuation theorem contexts

Enabled experimental testing of one-shot thermodynamic quantities

Abstract

Two approaches to small-scale and quantum thermodynamics are fluctuation relations and one-shot statistical mechanics. Fluctuation relations (such as Crooks' Theorem and Jarzynski's Equality) relate nonequilibrium behaviors to equilibrium quantities such as free energy. One-shot statistical mechanics involves statements about every run of an experiment, not just about averages over trials. We investigate the relation between the two approaches. We show that both approaches feature the same notions of work and the same notions of probability distributions over possible work values. The two approaches are alternative toolkits with which to analyze these distributions. To combine the toolkits, we show how one-shot work quantities can be defined and bounded in contexts governed by Crooks' Theorem. These bounds provide a new bridge from one-shot theory to experiments originally designed for testing fluctuation theorems.