# Quantum engine efficiency bound beyond the second law of thermodynamics

## TL;DR

This paper establishes a new efficiency bound for quantum engines powered by non-thermal baths, which extends beyond the traditional second law limits and is not solely derived from thermodynamics.

## Contribution

It derives a novel inequality for energy exchange that sets an efficiency limit for quantum engines with non-thermal baths, independent of reversibility.

## Key findings

- Quantum engines with non-thermal baths have an efficiency bound beyond the Carnot limit.
- The bound is derived from an inequality related to entropy change during energy exchange.
- This efficiency limit cannot be deduced solely from the laws of thermodynamics.

## Abstract

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.