# Efficiency of a cyclic quantum heat engine with finite-size baths

## TL;DR

This paper explores how the efficiency of a cyclic quantum heat engine depends on the size of the thermal baths, showing that maximum efficiency is only achievable with infinitely large baths and analyzing the trade-off between power and efficiency in finite systems.

## Contribution

It establishes a general inequality linking quantum heat engine efficiency to bath size and introduces a model analyzing power-efficiency trade-offs with finite-dimensional baths.

## Key findings

- Carnot efficiency requires infinite bath size
- Finite baths limit maximum efficiency
- Power-efficiency trade-off depends on system dimensions

## Abstract

In this paper we investigate the relationship between the efficiency of a cyclic quantum heat engine with the Hilbert space dimension of the thermal baths. By means of a general inequality, we show that the Carnot efficiency can be obtained only when both the hot and cold baths are infinitely large. By further introducing a specific model where the baths are constituted of ensembles of finite-dimensional particles, we further demonstrate the relationship between the engine's power and efficiency, with the dimension of the working substance and the bath particles.