Optimal performance of a three stroke heat engine in the microscopic regime

TL;DR

This paper derives the maximum work and efficiency of a microscopic three-stroke heat engine with a two-level system, considering both ideal and restricted thermal operations, bridging theoretical optimality and experimental feasibility.

Contribution

It provides closed-form expressions for maximum work and efficiency under restricted thermal operations, extending previous idealized models to more realistic scenarios.

Findings

Maximum work and efficiency formulas derived for restricted thermal operations.

Optimal performance matches ideal cases when restrictions are lifted.

Results applicable to experimental implementations with finite baths.

Abstract

We consider a three-stroke engine in the microscopic regime, where the working body of the engine is composed of a two-level system. The working body of the engine aims to withdraw heat from the hot heat bath, generate work, and discharge the surplus heat into the cold heat bath through the successive execution of three strokes. In this process, the interaction of the working body with the heat baths is assumed to be energy-conserving and thus can be described by thermal operations. While earlier studies analyzed the optimal performance of this engine when the working body could be transformed by any arbitrary thermal operation, we present closed expressions for the maximum work produced by the engine and the maximum efficiency of the engine when only a restricted class of thermal operations can be implemented on the working body. Furthermore, we explore the engine's optimal performance under two well-studied classes of restrictions: thermal operations realized via Jaynes-Cummings interaction and thermal operations realizable with finite-sized heat baths. Therefore, on one hand, our results are general, as they reproduce the optimal performance achieved when any arbitrary thermal operation can be implemented on the working body once the restriction is relaxed. On the other hand, our results allow us to determine the engine's maximum work production and efficiency in a more realistic scenario, where only a restricted class of thermal operations are possible, thereby bringing our findings closer to experimental feasibility.