Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory

Eglinton, Joshua; Carollo, Federico; Lesanovsky, Igor; Brandner, Kay

Abstract

Microscopic thermal machines promise to play an important role in future quantum technologies. Making such devices widely applicable will require effective strategies to channel their output into easily accessible storage systems like classical degrees of freedom. Here, we develop a self-consistent theoretical framework that makes it possible to model such quantum-classical hybrid devices in a thermodynamically consistent manner. Our approach is based on the assumption that the quantum part of the device is subject to strong decoherence and dissipation induced by a thermal reservoir. Due to the ensuing separation of time scales between slowly evolving classical and fast relaxing quantum degrees of freedom, the dynamics of the hybrid system can be described by means of adiabatic-response theory. We show that, upon including fluctuations in a minimally consistent way, the resulting equations of motion can be equipped with a first and second law, both on the ensemble level and on the level of individual trajectories of the classical part of the system, where thermodynamic quantities like heat and work become stochastic variables. As an application of our theory, we work out a physically transparent model of a quantum-classical hybrid engine, whose working system consists of a chain of Rydberg atoms, which is confined in an optical cavity and driven by periodic temperature variations. We demonstrate through numerical simulations that the engine can sustain periodic oscillations of a movable mirror, which acts as a classical load, against external friction and extract the full distributions of input heat and output work. By making the statistics of thermodynamic processes in quantum-classical hybrid systems accessible without the need to further specify a measurement protocol, our work contributes to bridging the long-standing gap between classical and quantum stochastic thermodynamics.

Citation

Eglinton, J., Carollo, F., Lesanovsky, I., & Brandner, K. (2024). Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory. Quantum, 8, Article 1486. https://doi.org/10.22331/q-2024-09-26-1486

• Journal Article Type: Article
• Acceptance Date: Sep 12, 2024
• Online Publication Date: Sep 26, 2024
• Publication Date: Sep 26, 2024
• Deposit Date: Oct 10, 2024
• Publicly Available Date: Oct 10, 2024
• Journal: Quantum
• Print ISSN: 2521-327X
• Electronic ISSN: 2521-327X
• Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
• Peer Reviewed: Peer Reviewed
• Volume: 8
• Article Number: 1486
• DOI: https://doi.org/10.22331/q-2024-09-26-1486
• Public URL: https://nottingham-repository.worktribe.com/output/40000396
• Publisher URL: https://quantum-journal.org/papers/q-2024-09-26-1486/