- Letter
- Open Access
Power fluctuations in a finite-time quantum Carnot engine
Phys. Rev. Research 3, L032041 – Published 13 August, 2021
DOI: https://doi.org/10.1103/PhysRevResearch.3.L032041
Abstract
Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space structure on its stability. We optimize in particular its relative work fluctuations with respect to level degeneracy and level number. We find that its optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results show how to realize high-performance, high-stability cyclic quantum heat engines.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (48)
- Y. A. Cengel and M. A. Boles, Thermodynamics. An Engineering Approach (McGraw-Hill, New York, 2001).
- I. A. Martinez, E. Roldan, L. Dinis, D. Petrov, J. M. R. Parrondo, and R. A. Rica, Brownian Carnot engine, Nat. Phys. 12, 67 (2015).
- F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43, 22 (1975).
- B. Andresen, R. S. Berry, A. Nitzan, and P. Salamon, Thermodynamics in finite time. I. The step-Carnot cycle, Phys. Rev. A 15, 2086 (1977).
- D. Gutkowicz-Krusin, I. Procaccia, and J. Ross, On the efficiency of rate processes. Power and efficiency of heat engines, J. Chem. Phys. 69, 3898 (1978).
- M. H. Rubin, Optimal configuration of a class of irreversible heat engines, Phys. Rev. A 19, 1277 (1979).
- P. Salamon and A. Nitzan, Finite time optimizations of a Newton's law Carnot cycle, J. Chem. Phys. 74, 3546 (1981).
- M. J. Ondrechen, M. H. Rubin, and Y. B. Band, The generalized Carnot cycle: A working fluid operating in finite time between finite heat sources and sinks, J. Chem. Phys. 78, 4721 (1983).
- M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Efficiency at Maximum Power of Low-Dissipation Carnot Engines, Phys. Rev. Lett. 105, 150603 (2010).
- V. Cavina, A. Mari, and V. Giovannetti, Slow Dynamics and Thermodynamics of Open Quantum Systems, Phys. Rev. Lett. 119, 050601 (2017).
- E. Geva and R. Kosloff, A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid, J. Chem. Phys. 96, 3054 (1992).
- E. Geva and R. Kosloff, On the classical limit of quantum thermodynamics in finite time, J. Chem. Phys. 97, 4398 (1992).
- F. Wu, L. Chen, S. Wu, F. Sun, and C. Wu, Performance of an irreversible quantum Carnot engine with spin 1/2, J. Chem. Phys. 124, 214702 (2006).
- H. T. Quan, Y. Liu, C. P. Sun, and F. Nori, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E 76, 031105 (2007).
- S. Abe, Maximum-power quantum-mechanical Carnot engine, Phys. Rev. E 83, 041117 (2011).
- J. Wang, J. He, and Z. Wu, Efficiency at maximum power output of quantum heat engines under finite-time operation, Phys. Rev. E 85, 031145 (2012).
- A. E. Allahverdyan, K. V. Hovhannisyan, A. V. Melkikh, and S. G. Gevorkian, Carnot Cycle at Finite Power: Attainability of Maximal Efficiency, Phys. Rev. Lett. 111, 050601 (2013).
- R. D. Dann and R. Kosloff, Quantum signatures in the quantum Carnot cycle, New J. Phys. 22, 013055 (2020).
- P. Abiuso and M. Perarnau-Llobet, Optimal Cycles for Low-Dissipation Heat Engines, Phys. Rev. Lett. 124, 110606 (2020).
- U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
- G. Verley, M. Esposito, T. Willaert, and C. Van den Broeck, The unlikely Carnot efficiency, Nat. Commun. 5, 4721 (2014).
- G. Verley, T. Willaert, C. Van den Broeck, and M. Esposito, Universal theory of efficiency fluctuations, Phys. Rev. E 90, 052145 (2014).
- M. Polettini, G. Verley, and M. Esposito, Efficiency Statistics at All Times: Carnot Limit at Finite Power, Phys. Rev. Lett. 114, 050601 (2015).
- S. K. Manikandan, L. Dabelow, R. Eichhorn, and S. Krishnamurthy, Efficiency Fluctuations in Microscopic Machines, Phys. Rev. Lett. 122, 140601 (2019).
- V. Holubec, An exactly solvable model of a stochastic heat engine: optimization of power, power fluctuations and efficiency, J. Stat. Mech. (2014) P05022.
- V. Holubec and A. Ryabov, Work and power fluctuations in a critical heat engine, Phys. Rev. E 96, 030102(R) (2017).
- P. Pietzonka and U. Seifert, Universal Trade-Off between Power, Efficiency and Constancy in Steady-State Heat Engines, Phys. Rev. Lett. 120, 190602 (2018).
- V. Holubec and A. Ryabov, Cycling Tames Power Fluctuations near Optimum Efficiency, Phys. Rev. Lett. 121, 120601 (2018).
- C. J. Foot, Atomic Physics (Oxford University Press, Oxford, UK, 2005).
- R. L. Brooks, The Fundamentals of Atomic and Molecular Physics (Springer, Berlin, 2013).
- P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, UK, 2000).
- V. Bazani, A. Credi, and M. Venturi, Molecular Devices and Machines (Wiley-VCH, Weinheim, 2003).
- S. J. Blundell and K. M. Blundell, Concepts in Thermal Physics (Oxford University Press, Oxford, UK, 2006).
- M. Evangelisti, F. Luis, L. J. de Jongh, and M. Affronte, Magnetothermal properties of molecule-based materials, J. Mater. Chem. 16, 2534 (2006).
- B. Everitt, The Cambridge Dictionary of Statistics (Cambridge University Press, Cambridge, UK, 1998).
- V. Gritsev, P. Barmettler, and E. Demler, Scaling approach to quantum non-equilibrium dynamics of many-body systems, New J. Phys. 12, 113005 (2010).
- C. Jarzynski, Generating shortcuts to adiabaticity in quantum and classical dynamics, Phys. Rev. A 88, 040101(R) (2013).
- A. del Campo, Shortcuts to Adiabaticity by Counterdiabatic Driving, Phys. Rev. Lett. 111, 100502 (2013).
- S. Deffner, C. Jarzynski, and A. del Campo, Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving, Phys. Rev. X 4, 021013 (2014).
- M. Beau, J. Jaramillo, and A. del Campo, Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity, Entropy 18, 168 (2016).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032041 for details about the derivation of the work distribution and of the coefficients of variation of work.
- P. Talkner, E. Lutz, and P. Hänggi, Fluctuation theorems: Work is not an observable, Phys. Rev. E 75, 050102(R) (2007).
- A. E. Allahverdyan, R. S. Johal, and G. Mahler, Work extremum principle: Structure and function of quantum heat engines, Phys. Rev. E 77, 041118 (2008).
- D. Gelbwaser-Klimovsky, W. Niedenzu, P. Brumer, and G. Kurizki, Power enhancement of heat engines via correlated thermalization in a three-level “working fluid”, Sci. Rep. 5, 14413 (2015).
- W. Niedenzu, D. Gelbwaser-Klimovsky, and G. Kurizki, Performance limits of multilevel and multipartite quantum heat machines, Phys. Rev. E 92, 042123 (2015).
- H. T. Quan, P. Zhang, and C. P. Sun, Quantum heat engine with multilevel quantum systems, Phys. Rev. E 72, 056110 (2005).
- J. Wang and J. He, Optimization on a three-level heat engine working with two noninteracting fermions in a one-dimensional box trap, J. Appl. Phys. 111, 043505 (2012).
- R. Wang, J. Wang, J. He, and Y. Ma, Performance of a multilevel quantum heat engine of an ideal -particle Fermi system, Phys. Rev. E 86, 021133 (2012).