Periodically-driven quantum thermal machines from warming up to limit cycle

TL;DR

This paper develops a comprehensive thermodynamic framework for periodically-driven quantum thermal machines that accounts for their behavior before and during the limit-cycle, highlighting the importance of a new contribution to the first law especially at strong system-bath couplings.

Contribution

It introduces a novel thermodynamic description that captures the entire operational regime of PD-QTMs, including non-limit-cycle phases and strong coupling effects.

Findings

A new thermodynamic contribution is necessary for a complete first law description.

The contribution is significant at strong couplings, affecting efficiency.

Simulation of a quantum Otto engine demonstrates the framework's applicability.

Abstract

Theoretical treatments of periodically-driven quantum thermal machines (PD-QTMs) are largely focused on the limit-cycle stage of operation characterized by a periodic state of the system. Yet, this regime is not immediately accessible for experimental verification. Here, we present a general thermodynamic framework that can handle the performance of PD-QTMs both before and during the limit-cycle stage of operation. It is achieved by observing that periodicity may break down at the ensemble average level, even in the limit-cycle phase. With this observation, and using conventional thermodynamic expressions for work and heat, we find that a complete description of the first law of thermodynamics for PD-QTMs requires a new contribution, which vanishes only in the limit-cycle phase under rather weak system-bath couplings. Significantly, this contribution is substantial at strong couplings even at limit cycle, thus largely affecting the behavior of the thermodynamic efficiency. We demonstrate our framework by simulating a quantum Otto engine building upon a driven resonant level model. Our results provide new insights towards a complete description of PD-QTMs, from turn-on to the limit-cycle stage and, particularly, shed light on the development of quantum thermodynamics at strong coupling.