Informative priors and the analogy between quantum and classical heat engines

TL;DR

This paper explores the connection between quantum and classical heat engines under incomplete information, revealing similar prior distributions and efficiency behaviors near equilibrium.

Contribution

It introduces a unified perspective on quantum and classical heat engines using a common prior distribution for uncertain parameters.

Findings

Prior distribution in both models is proportional to 1/x.

Expected efficiency approaches one third of Carnot efficiency near equilibrium.

Quantum and classical models share similar information-theoretic structures.

Abstract

When incomplete information about the control parameters is quantified as a prior distribution, a subtle connection emerges between quantum heat engines and their classical analogs. We study the quantum model where the uncertain parameters are the intrinsic energy scales and compare with the classical models where the intermediate temperature is the uncertain parameter. The prior distribution quantifying the incomplete information has the form $\pi(x)\propto 1/x$ in both the quantum and the classical models. The expected efficiency calculated in near-equilibrium limit approaches the value of one third of Carnot efficiency.