Catalytic enhancement in the performance of the microscopic two-stroke heat engine
Abstract: We consider a model of heat engine operating in the microscopic regime: the two-stroke engine. It produces work and exchanges heat in two discrete strokes that are separated in time. The working body of the engine consists of two $d$-level systems initialized in thermal states at two distinct temperatures. Additionally, an auxiliary non-equilibrium system called catalyst may be incorporated with the working body of the engine, provided the state of the catalyst remains unchanged after the completion of a thermodynamic cycle. This ensures that the work produced by the engine arises solely from the temperature difference. Upon establishing the rigorous thermodynamic framework, we characterize two-fold improvement stemming from the inclusion of a catalyst. Firstly, we prove that in the non-catalytic scenario, the optimal efficiency of the two-stroke heat engine with a working body composed of two-level systems is given by the Otto efficiency, which can be surpassed by incorporating a catalyst with the working body. Secondly, we show that incorporating a catalyst allows the engine to operate in frequency and temperature regimes that are not accessible for non-catalytic two-stroke engines. We conclude with general conjecture about advantage brought by catalyst: including the catalyst with the working body always allows to improve efficiency over the non-catalytic scenario for any microscopic two-stroke heat engines. We prove the conjecture for two-stroke engines when the working body is composed of two $d$-level systems initialized in thermal states at two distinct temperatures, as long as the final joint state leading to optimal efficiency in the non-catalytic scenario is not product, or at least one of the $d$-level system is not thermal.
- N. Shiraishi and T. Sagawa, Quantum thermodynamics of correlated-catalytic state conversion at small scale, Phys. Rev. Lett. 126, 150502 (2021).
- H. Wilming, Entropy and reversible catalysis, Phys. Rev. Lett. 127, 260402 (2021).
- P. Lipka-Bartosik, H. Wilming, and N. H. Y. Ng, Catalysis in quantum information theory, arXiv:2306.00798 (2023).
- I. Henao and R. Uzdin, Catalytic leverage of correlations and mitigation of dissipation in information erasure, Phys. Rev. Lett. 130, 020403 (2023).
- I. Henao and R. Uzdin, Catalytic transformations with finite-size environments: applications to cooling and thermometry, Quantum 5, 547 (2021).
- C. Sparaciari, D. Jennings, and J. Oppenheim, Energetic instability of passive states in thermodynamics, Nature Communications 8, 1895 (2017).
- N. F. Ramsey, Thermodynamics and statistical mechanics at negative absolute temperatures, Phys. Rev. 103, 20 (1956).
- H. E. D. Scovil and E. O. Schulz-DuBois, Three-level masers as heat engines, Phys. Rev. Lett. 2, 262 (1959).
- J. E. Geusic, E. O. Schulz-DuBios, and H. E. D. Scovil, Quantum equivalent of the carnot cycle, Phys. Rev. 156, 343 (1967).
- R. Kosloff, A quantum mechanical open system as a model of a heat engine, J. Chem. Phys. 80, 10.1063/1.446862 (1984).
- R. Kosloff and A. Levy, Quantum heat engines and refrigerators: Continuous devices, Annual Review of Physical Chemistry 65, 365 (2014a), pMID: 24689798, https://doi.org/10.1146/annurev-physchem-040513-103724 .
- M. O. Scully, Quantum afterburner: Improving the efficiency of an ideal heat engine, Phys. Rev. Lett. 88, 050602 (2002).
- N. Linden, S. Popescu, and P. Skrzypczyk, How small can thermal machines be? the smallest possible refrigerator, Phys. Rev. Lett. 105, 130401 (2010a).
- A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Maximal work extraction from finite quantum systems, Europhysics Letters (EPL) 67, 565 (2004).
- D. Segal and A. Nitzan, Molecular heat pump, Phys. Rev. E 73, 026109 (2006).
- M. J. Henrich, G. Mahler, and M. Michel, Driven spin systems as quantum thermodynamic machines: Fundamental limits, Phys. Rev. E 75, 051118 (2007).
- N. Linden, S. Popescu, and P. Skrzypczyk, The smallest possible heat engines, arXiv:1010.6029 (2010b).
- N. M. Myers, O. Abah, and S. Deffner, Quantum thermodynamic devices: From theoretical proposals to experimental reality, AVS Quantum Science 4, 027101 (2022), https://pubs.aip.org/avs/aqs/article-pdf/doi/10.1116/5.0083192/16494008/027101_1_online.pdf .
- W. Pusz and S. L. Woronowicz, Passive states and kms states for general quantum systems, Comm. Math. Phys. 58, 273 (1978).
- R. Alicki, The quantum open system as a model of the heat engine, J. Phys. A: Math. Gen. 12, L103 (1979).
- P. C. W. Davies, Thermodynamics of black holes, Reports on Progress in Physics 41, 1313 (1978).
- M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013).
- P. Skrzypczyk, A. J. Short, and S. Popescu, Work extraction and thermodynamics for individual quantum systems, Nat. Commun. 5, 4185 (2014).
- V. Blickle and C. Bechinger, Realization of a micrometre-sized stochastic heat engine, Nature Physics 8, 143 (2011).
- A. E. Allahverdyan, K. Hovhannisyan, and G. Mahler, Optimal refrigerator, Phys. Rev. E 81, 051129 (2010).
- M. T. Mitchison, Quantum thermal absorption machines: refrigerators, engines and clocks, Contemporary Physics 60, 164 (2019), https://doi.org/10.1080/00107514.2019.1631555 .
- M. P. Woods, N. H. Y. Ng, and S. Wehner, The maximum efficiency of nano heat engines depends on more than temperature, Quantum 3, 177 (2019).
- R. Kosloff and A. Levy, Quantum heat engines and refrigerators: Continuous devices, Annual Review of Physical Chemistry 65, 365 (2014b).
- S. Popescu, Maximally efficient quantum thermal machines: The basic principles, arXiv:1009.2536 (2010).
- M. Łobejko, P. Mazurek, and M. Horodecki, Thermodynamics of Minimal Coupling Quantum Heat Engines, Quantum 4, 375 (2020).
- W. Niedenzu, M. Huber, and E. Boukobza, Concepts of work in autonomous quantum heat engines, Quantum 3, 195 (2019).
- K. Ptaszyński, Non-markovian thermal operations boosting the performance of quantum heat engines, Phys. Rev. E 106, 014114 (2022).
- J. Czartowski, A. de Oliveira Junior, and K. Korzekwa, Thermal recall: Memory-assisted markovian thermal processes, PRX Quantum 4, 040304 (2023).
- C. S. Yu, B. Q. Guo, and T. Liu, Quantum self-contained refrigerator in terms of the cavity quantum electrodynamics in the weak internal-coupling regime, Opt. Express 27, 6863 (2019).
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