Thermodynamic Approach to Quantifying Incompatible Instruments

TL;DR

This paper introduces a thermodynamic framework to quantify instrument incompatibility using thermalisation time and work extraction, revealing their equivalence and the disappearance of incompatibility signatures in non-Markovian thermalisation.

Contribution

It proposes a novel thermodynamic resource theory approach to measure instrument incompatibility through thermalisation time and work extraction, linking these concepts.

Findings

Thermalisation time equals incompatibility advantage in work extraction.

Incompatibility signatures vanish in non-Markovian thermalisation.

Thermodynamic measures can quantify instrument incompatibility.

Abstract

We consider a thermodynamic framework to quantify instrument incompatibility via a resource theory subject to thermodynamic constraints. We use the minimal thermalisation time needed to erase incompatibility's signature to measure incompatibility. Unexpectedly, this time value is equivalent to incompatibility advantage in a work extraction task. Hence, both thermalisation time and extractable work can directly quantify instrument incompatibility. Finally, we show that incompatibility signatures must vanish in non-Markovian thermalisation.