Precision bound and optimal control in periodically modulated continuous quantum thermal machines

TL;DR

This paper develops a Floquet-based theoretical framework to analyze fluctuations and bounds in efficiencies of periodically modulated quantum thermal machines, revealing how modulation schemes influence thermodynamic uncertainty relations and machine performance.

Contribution

It introduces a generic Floquet formalism for quantum thermal machines and explores the impact of various modulation schemes on fluctuations and thermodynamic bounds.

Findings

TUR holds for all modulation types studied.

Sinusoidal modulation minimizes TUR ratio at heat engine-refrigerator transition.

CRAB optimization maintains low TUR ratio across frequencies.

Abstract

We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the Chopped Random Basis (CRAB) optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator, and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.