# Concepts of work in autonomous quantum heat engines

## TL;DR

This paper explores various concepts of work in quantum heat engines, analyzing their operational meanings and efficiencies, especially in the context of a three-level maser, highlighting differences from classical thermodynamics.

## Contribution

It provides a comparative analysis of different quantum work quantifiers and derives efficiencies for a quantum heat engine using a three-level maser model.

## Key findings

- Engine efficiency converges to classical limit at high intensities.
- Different work quantifiers have distinct operational interpretations.
- Quantum entropy considerations affect work definitions in quantum engines.

## Abstract

One of the fundamental questions in quantum thermodynamics concerns the decomposition of energetic changes into heat and work. Contrary to classical engines, the entropy change of the piston cannot be neglected in the quantum domain. As a consequence, different concepts of work arise, depending on the desired task and the implied capabilities of the agent using the work generated by the engine. Each work quantifier---from ergotropy to non-equilibrium free energy---has well defined operational interpretations. We analyse these work quantifiers for a heat-pumped three-level maser and derive the respective engine efficiencies. In the classical limit of strong maser intensities the engine efficiency converges towards the Scovil--Schulz-DuBois maser efficiency, irrespective of the work quantifier.