Thermodynamic uncertainty relation in slowly driven quantum heat engines

TL;DR

This paper derives a new thermodynamic uncertainty relation for slowly driven quantum heat engines, showing they can operate near Carnot efficiency with finite power and small fluctuations, even considering quantum effects.

Contribution

It introduces an alternative TUR for periodically driven quantum engines, less restrictive than steady-state TURs, and accounts for quantum fluctuations affecting efficiency.

Findings

Engine can operate close to Carnot efficiency with finite power.

Quantum fluctuations reduce efficiency and reliability.

New TUR applies to slow-driving quantum heat engines.

Abstract

Thermodynamic Uncertainty Relations express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for autonomous heat engines operating at steady-state, imposing an upper bound for their efficiency in terms of the power yield and its fluctuations. In the present manuscript we analyse a different class of heat engines, namely those which are operating in the periodic slow-driving regime. We show that an alternative TUR is satisfied, which is less restrictive than that of steady-state engines: it allows for engines that produce finite power, with small power fluctuations, to operate close to the Carnot efficiency. The bound further incorporates the effect of quantum fluctuations, which reduces engine efficiency relative to the average power and reliability. We finally illustrate our findings in the experimentally relevant model of a single-ion heat engine.