Thermodynamics of Minimal Coupling Quantum Heat Engines

Marcin Łobejko1, Paweł Mazurek1,2, and Michał Horodecki1,2

1Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland
2International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland

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The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.

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Cited by

[1] Patryk Lipka-Bartosik and Paul Skrzypczyk, "All States are Universal Catalysts in Quantum Thermodynamics", Physical Review X 11 1, 011061 (2021).

[2] Marcin Łobejko, "The tight Second Law inequality for coherent quantum systems and finite-size heat baths", Nature Communications 12 1, 918 (2021).

[3] Patryk Lipka-Bartosik, Paweł Mazurek, and Michał Horodecki, "Second law of thermodynamics for batteries with vacuum state", Quantum 5, 408 (2021).

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