We consider a quantum endoreversible Carnot engine cycle and its inverse operation–Carnot refrigeration cycle, working between a hot bath of inverse temperature and a cold bath at inverse temperature . For the engine model, the hot bath is constructed to be squeezed, whereas for the refrigeration cycle, the cold bath is set to be squeezed. In the high-temperature limit, we analyze efficiency at maximum power and coefficient of performance at maximum figure of merit, revealing the effects of the times allocated to two thermal-contact and two adiabatic processes on the machine performance. We show that, when the total time spent along the two adiabatic processes is negligible, the efficiency at maximum power reaches its upper bound, which can be analytically expressed in terms of squeezing parameter : , with the Carnot efficiency and the coefficient of performance at maximum figure of merit is bounded from the upper side by the analytical function: , where .
REFERENCES
1.
F.
Curzon
and B.
Ahlborn
, “Efficiency of a Carnot engine at maximum power output
,” Am. J. Phys.
43
, 22
(1975
). 2.
J.
Chen
, “The maximum power output and maximum efficiency of an irreversible Carnot heat engine
,” J. Phys. D: Appl. Phys.
27
, 1144
(1994
). 3.
E.
Geva
and R.
Kosloff
, “A quantum-mechanical heat engine operating in finite time. A model consisting of spin- systems as the working fluid
,” J. Chem. Phys.
96
, 3054
(1992
); “
On the classical limit of quantum thermodynamics in finite time
,” ibid.
97
, 4398
(1992
). 4.
C.
Van den Broeck
, “Thermodynamic efficiency at maximum power
,” Phys. Rev. Lett.
95
, 190602
(2005
). 5.
Y.
Izumida
and K.
Okuda
, “Molecular kinetic analysis of a finite-time Carnot cycle
,” Europhys. Lett.
83
, 60003
(2008
); “
Numerical experiments of a finite-time thermodynamic cycle,
” Prog. Theor. Phys. Suppl.
178
, 163
(2009
). 6.
M.
Esposito
, K.
Lindenberg
, and C.
Van den Broeck
, “Thermoelectric efficiency at maximum power in a quantum dot
,” Europhys. Lett.
85
, 60010
(2009
); B.
Rutten
, M.
Esposito
, and B.
Cleuren
, “Reaching optimal efficiencies using nanosized photoelectric devices,
” Phys. Rev. B
80
, 235122
(2009
); M.
Esposito
, R.
Kawai
, K.
Lindenberg
, and C.
Van den Broeck
, “Quantum-dot Carnot engine at maximum power,
” Phys. Rev. E
81
, 041106
(2010
). 7.
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
). 8.
J. H.
Wang
and J. Z.
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
). 9.
R.
Kosloff
, “Quantum thermodynamics: A dynamical viewpoint
,” Entropy
15
, 2100
(2013
). 10.
R.
Kosloff
and A.
Levy
, “Quantum heat engines and refrigerators: Continuous devices
,” Annu. Rev. Phys. Chem.
65
, 365
(2014
). 11.
R.
Long
, Z.
Liu
, and W.
Liu
, “Performance optimization of minimally nonlinear irreversible heat engines and refrigerators under a trade-off figure of merit
,” Phys. Rev. E
89
, 062119
(2014
). 12.
S.
Çakmak
, M.
Çandır
, and F.
Altintas
, “Construction of a quantum Carnot heat engine cycle
,” Quantum Inf. Process.
19
, 314
(2020
). 13.
S.
Çakmak
and F.
Altintas
, “Quantum Carnot cycle with inner friction
,” Quantum Inf. Process.
19
, 248
(2020
). 14.
S.
Çakmak
and F.
Altintas
, “Different constructions and optimization of the irreversible quantum Carnot cycle
,” Eur. Phys. J. Plus
136
, 369
(2021
). 15.
S.
Çakmak
, “A feasible quantum heat engine driven by dipole-dipole interaction
,” Phys. Lett. A
422
, 127796
(2022
). 16.
Z.
Yan
and J.
Chen
, “A class of irreversible Carnot refrigeration cycles with a general heat transfer law
,” J. Phys. D: Appl. Phys.
23
, 136
(1990
). 17.
A. E.
Allahverdyan
, K.
Hovhannisyan
, and G.
Mahler
, “Optimal refrigerator
,” Phys. Rev. E
81
, 051129
(2010
). 18.
Y.
Apertet
, H.
Ouerdane
, A.
Michot
, C.
Goupil
, and Ph.
Lecoeur
, “On the efficiency at maximum cooling power
,” Europhys. Lett.
103
, 40001
(2013
). 19.
Z.
Yan
and J.
Chen
, “Transition from streamer to Townsend mechanisms in dielectric voids
,” J. Phys. D
23
, 136
(1990
). 20.
S.
Velasco
, J. M. M.
Roco
, A.
Medina
, and A. C.
Hernandez
, “New performance bounds for a finite-time Carnot refrigerator
,” Phys. Rev. Lett.
78
, 3241
(1997
). 21.
C.
de Tomas
, J. M. M.
Roco
, A. C.
Hernandez
, Y.
Wang
, and Z. C.
Tu
, “Low-dissipation heat devices: Unified trade-off optimization and bounds
,” Phys. Rev. E
87
, 012105
(2013
). 22.
C.
de Tomás
, A.
Calvo Hernández
, and J. M. M.
Roco
, “Optimal low symmetric dissipation Carnot engines and refrigerators
,” Phys. Rev. E
85
, 010104(R)
(2012
). 23.
Y.
Wang
, M.
Li
, Z. C.
Tu
, A. C.
Hernandez
, and J. M. M.
Roco
, “Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators
,” Phys. Rev. E
86
, 011127
(2012
). 24.
Y.
Hu
, F.
Wu
, Y.
Ma
, J.
He
, J.
Wang
, A. C.
Hernández
, and J. M. M.
Roco
, “Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation
,” Phys. Rev. E
88
, 062115
(2013
). 25.
Y.
Yuan
, R.
Wang
, J.
He
, Y.
Ma
, and J.
Wang
, “Coefficient of performance under maximum criterion in a two-level atomic system as a refrigerator
,” Phys. Rev. E
90
, 052151
(2014
). 26.
Y.
Izumida
, K.
Okuda
, A.
Calvo Hernández
, and J. M. M.
Roco
, “Coefficient of performance under optimized figure of merit in minimally nonlinear irreversible refrigerator
,” Europhys. Lett.
101
, 10005
(2013
). 27.
Y. C.
Zhang
, “Optimization performance of quantum Otto heat engines and refrigerators with squeezed thermal reservoirs
,” Physica A
559
, 125083
(2020
). 28.
J. H.
Wang
, J. Z.
He
, and Y. L.
Ma
, “Finite-time performance of a quantum heat engine with a squeezed thermal bath
,” Phys. Rev. E
100
, 052126
(2019
). 29.
J.
Klaers
, S.
Faelt
, A.
Imamoglu
, and E.
Togan
, “Squeezed thermal reservoirs as a resource for a nanomechanical engine beyond the Carnot limit
,” Phys. Rev. X
7
, 031044
(2017
). 30.
J. H.
Jiang
, “Enhancing efficiency and power of quantum-dots resonant tunneling thermoelectrics in three-terminal geometry by cooperative effects
,” J. Appl. Phys.
116
, 194303
(2014
). 31.
R.
Kosloff
and Y.
Rezek
, “The quantum harmonic Otto cycle
,” Entropy
19
, 136
(2017
). 32.
J.
Rofinagel
, O.
Abah
, F.
Schmidt-Kaler
, K.
Singer
, and E.
Lutz
, “Nanoscale heat engine beyond the Carnot limit
,” Phys. Rev. Lett.
112
, 030602
(2014
). 33.
R.
Uzdin
, R. A.
Levy
, and R.
Kosloff
, “Equivalence of quantum heat machines, and quantum-thermodynamic signatures
,” Phys. Rev. X
5
, 31044
(2015
). 34.
J.
Guo
, J.
Wang
, Y.
Wang
, and J.
Chen
, “Efficiencies of two-level weak dissipation quantum Carnot engines at the maximum power output
,” J. Appl. Phys.
113
, 143510
(2013
). 35.
V.
Singh
and Ö. E.
Müstecaplıoǧlu
, “Performance bounds of nonadiabatic quantum harmonic Otto engine and refrigerator under a squeezed thermal reservoir
,” Phys. Rev. E
102
, 062123
(2020
). 36.
Z.
Wang
, L.
Wang
, J.
Chen
, C.
Wang
, and J.
Ren
, “Geometric heat pump: Controlling thermal transport with time-dependent modulations
,” Front. Phys.
17
, 13201
(2022
). 37.
J.
Lu
, R.
Wang
, Y.
Liu
, and J. H.
Jiang
, “Thermoelectric cooperative effect in three-terminal elastic transport through a quantum dot
,” J. Appl. Phys.
122
, 044301
(2017
). 38.
S. H.
Raja
, S.
Maniscalco
, G. S.
Paraoanu
, J. P.
Pekola
, and N. L.
Gullo
, “Finite-time quantum Stirling heat engine
,” New J. Phys.
23
, 033034
(2021
). 39.
M.
Campisi
, J.
Pekola
, and R.
Fazio
, “Nonequilibrium fluctuations in quantum heat engines: Theory, example, and possible solid state experiments
,” New J. Phys.
17
, 035012
(2015
). 40.
H. T.
Quan
, Y. X.
Liu
, C. P.
Sun
, and F.
Nori
, “Quantum thermodynamic cycles and quantum heat engines
,” Phys. Rev. E
76
, 031105
(2007
); H. T.
Quan
, “Quantum thermodynamic cycles and quantum heat engines,
” ibid.
79
, 041129
(2009
). 41.
J. H.
Wang
, Y. L.
Ma
, and J. Z.
He
, “Quantum-mechanical engines working with an ideal gas with a finite number of particles confined in a power-law trap
,” Eur. Phys. Lett.
111
, 20006
(2015
). 42.
D.
Gelbwaser-Klimovsky
, A.
Bylinskii
, D.
Gangloff
, R.
Islam
, A.
Aspuru-Guzik
, and V.
Vuletic
, “Single-atom heat machines enabled by energy quantization
,” Phys. Rev. Lett.
120
, 170601
(2018
). 43.
W.
Niedenzu
, V.
Mukherjee
, A.
Ghosh
, A. G.
Kofman
, and G.
Kurizki
, “Quantum engine efficiency bound beyond the second law of thermodynamics
,” Nat. Commun.
9
, 165
(2018
). 44.
X. L.
Huang
, T.
Wang
, and X. X.
Yi
, “Effects of reservoir squeezing on quantum systems and work extraction
,” Phys. Rev. E
86
, 051105
(2012
). 45.
M.
Kim
, F.
De Oliveira
, and P.
Knight
, “Properties of squeezed number states and squeezed thermal states
,” Phys. Rev. A
40
, 2494
(1989
). 46.
R.
Long
and W.
Liu
, “Performance of quantum Otto refrigerators with squeezing
,” Phys. Rev. E
91
, 062137
(2015
). 47.
G.
Manzano
, F.
Galve
, R.
Zambrini
, and J. M.
Parrondo
, “Entropy production and thermodynamic power of the squeezed thermal reservoir
,” Phys. Rev. E
93
, 052120
(2016
). 48.
W.
Niedenzu
, D.
Gelbwaser-Klimovsky
, A. G.
Kofman
, and G.
Kurizki
, “On the operation of machines powered by quantum non-thermal baths
,” New J. Phys.
18
, 083012
(2016
). 49.
M.
Esposito
and C.
Van den Broeck
, “Three faces of the second law. I. Master equation formulation
,” Phys. Rev. E
82
, 011143
(2010
). 50.
Y.
Rezek
and R.
Kosloff
, “Irreversible performance of a quantum harmonic heat engine
,” New J. Phys.
8
, 83
(2006
). 51.
J.
Wang
, Z. Q.
Wu
, and J. Z.
He
, “Quantum Otto engine of a two-level atom with single-mode fields
,” Phys. Rev. E
85
, 041148
(2012
). 52.
F.
Galve
and E.
Lutz
, “Nonequilibrium thermodynamic analysis of squeezing
,” Phys. Rev. A
79
, 055804
(2009
). 53.
A. M.
Zagoskin
, E.
Il’ichev
, and F.
Nori
, “Heat cost of parametric generation of microwave squeezed states
,” Phys. Rev. A
85
, 063811
(2012
). © 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
