A Study in Thermal: Advantage framework for resource engines

TL;DR

This paper formalizes a resource theory framework for thermal engines, analyzing their efficiency and operational bounds under various restrictions, and introduces tree-states for simplified engine analysis.

Contribution

It develops a comprehensive resource theory for thermal engines, including efficiency measures and bounds under different operational restrictions, with new constructs like tree-states.

Findings

Derived analytic lower bounds for engine operation

Provided a full description of engines under semilocal thermal operations

Introduced tree-states as simplified free states for analysis

Abstract

Thermal engines have been one of the principal topics of thermodynamics ever since its beginning. Today, in the era of the second quantum revolution, although the thermal processes in constant temperatures are relatively well understood in the language of resource theories, a framework to describe thermal engines is still in its infancy. In this work we formalize the resource theory of engines, initially put forward in [Quantum 8, 1222], and define such quantities as engine efficiency. Then, we turn to a detailed study of thermal engines based on free operations arising from the resource theory of athermality under different restrictions: thermal operation, semilocal thermal operations and local thermal operation with classical communication. In order to provide analytic lower bounds for thermal engine operation we construct tree-states -- free states, which can be obtained from Gibbs state in simple protocol consisting solely of two-level operations. Furthermore, we derive a full description of the engine based on semilocal thermal operations describing e.g. free states, faithful monotones and catalytic advantages.