Universal efficiency at optimal work with Bayesian statistics

TL;DR

This paper explores how Bayesian priors influence the efficiency of quantum heat engines, revealing that certain priors lead to optimal work at efficiencies close to the Curzon-Ahlborn value, highlighting a link between information and thermodynamics.

Contribution

It introduces a Bayesian framework to analyze quantum heat engine efficiency, demonstrating how prior distributions affect optimal work and efficiency near equilibrium.

Findings

Optimal work occurs at Curzon-Ahlborn efficiency when averaging over specific priors.

Efficiency scales as half of Carnot efficiency near equilibrium for certain priors.

Bayesian posterior estimates relate closely to classical thermodynamic formulas.

Abstract

If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a) \propto 1/a^{\gamma}$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes' theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a new connection between thermodynamic behavior and the concept of information.