{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T17:03:15Z","timestamp":1761930195402,"version":"build-2065373602"},"reference-count":97,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T00:00:00Z","timestamp":1619481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51779262"],"award-info":[{"award-number":["51779262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.<\/jats:p>","DOI":"10.3390\/e23050536","type":"journal-article","created":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T21:18:20Z","timestamp":1619558300000},"page":"536","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-6736","authenticated-orcid":false,"given":"Lingen","family":"Chen","sequence":"first","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zewei","family":"Meng","sequence":"additional","affiliation":[{"name":"College of Power Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanlin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"School of Mechanical &amp; Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1063\/1.434122","article-title":"Thermodynamics in finite time: Extremals for imperfect heat engines","volume":"66","author":"Andresen","year":"1977","journal-title":"J. Chem. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1021\/ar00104a001","article-title":"Thermodynamics for processes in finite time","volume":"17","author":"Andresen","year":"1984","journal-title":"Acc. Chem. Res."},{"key":"ref_3","first-page":"327","article-title":"Finite Time Thermodynamic Optimization or Entropy Generation Minimization of Energy Systems","volume":"22","author":"Chen","year":"1999","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1002\/anie.201001411","article-title":"Current Trends in Finite-Time Thermodynamics","volume":"50","author":"Andresen","year":"2011","journal-title":"Angew. Chem. Int. Ed."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/JNETDY.2003.015","article-title":"Optimal Process Paths for Endoreversible Systems","volume":"28","author":"Hoffmann","year":"2003","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Tang, C.Q., Feng, H.J., and Ge, Y.L. (2020). Power, efficiency, power density and ecological function optimizations for an irreversible modified closed variable-temperature reservoir regenerative Brayton cycle with one isothermal heating process. Energies, 13.","DOI":"10.3390\/en13195133"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Masser, R., and Hoffmann, K.H. (2020). Endoreversible modeling of a hydraulic recuperation system. Entropy, 22.","DOI":"10.3390\/e22040383"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tang, C.Q., Chen, L.G., Feng, H.J., Wang, W.H., and Ge, Y.L. (2020). Power optimization of a closed binary Brayton cycle with isothermal heating processes and coupled to variable-temperature reservoirs. Energies, 13.","DOI":"10.3390\/en13123212"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Masser, R., Khodja, A., Scheunert, M., Schwalbe, K., Fischer, A., Paul, R., and Hoffmann, K.H. (2020). Optimized piston motion for an alpha-type Stirling engine. Entropy, 22.","DOI":"10.3390\/e22060700"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Ge, Y.L., and Feng, H.J. (2020). Re-optimization of expansion work of a heated working fluid with generalized radiative heat transfer law. Entropy, 22.","DOI":"10.3390\/e22070720"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tsirlin, A., and Gagarina, L. (2020). Finite-time thermodynamics in economics. Entropy, 22.","DOI":"10.3390\/e22080891"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Tsirlin, A., and Sukin, I. (2020). Averaged optimization and finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22090912"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Muschik, W., and Hoffmann, K.H. (2020). Modeling, simulation, and reconstruction of 2-reservoir heat-to-power processes in finite-time thermodynamics. Entropy, 22.","DOI":"10.3390\/e22090997"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Andresen, B., and Essex, C. (2020). Thermodynamics at very long time and space scales. Entropy, 22.","DOI":"10.3390\/e22101090"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Shi, S.S., Ge, Y.L., Chen, L.G., and Feng, F.J. (2020). Four objective optimization of irreversible Atkinson cycle based on NSGA-II. Entropy, 22.","DOI":"10.3390\/e22101150"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, L.G., Ma, K., Feng, H.J., and Ge, Y.L. (2020). Optimal configuration of a gas expansion process in a piston-type cylinder with generalized convective heat transfer law. Energies, 13.","DOI":"10.3390\/en13123229"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Scheunert, M., Masser, R., Khodja, A., Paul, R., Schwalbe, K., Fischer, A., and Hoffmann, K.H. (2020). Power-optimized sinusoidal piston motion and its performance gain for an Alpha-type Stirling engine with limited regeneration. Energies, 13.","DOI":"10.3390\/en13174564"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1515\/jnet-2019-0078","article-title":"Evaluation of Irreversibility and Optimal Organization of an Integrated Multi-Stream Heat Exchange System","volume":"45","author":"Boykov","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"113261","DOI":"10.1016\/j.enconman.2020.113261","article-title":"Maximum energy output chemical pump configuration with an infinite-low- and a finite-high-chemical potential mass reservoirs","volume":"223","author":"Chen","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_20","first-page":"311","article-title":"Endoreversible thermodynamics","volume":"22","author":"Hoffmann","year":"1997","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1515\/jnet-2019-0063","article-title":"Stochastic Novikov engine with Fourier heat transport","volume":"44","author":"Schwalbe","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yasunaga, T., and Ikegami, Y. (2020). Finite-time thermodynamic model for evaluating heat engines in ocean thermal energy conversion. Entropy, 22.","DOI":"10.3390\/e22020211"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Feidt, M. (2020). Carnot cycle and heat engine: Fundamentals and applications. Entropy, 22.","DOI":"10.3390\/e22030348"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Feidt, M., and Costea, M. (2020). Effect of machine entropy production on the optimal performance of a refrigerator. Entropy, 22.","DOI":"10.3390\/e22090913"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Ma, Y.-H. (2020). Effect of finite-size heat source\u2019s heat capacity on the efficiency of heat engine. Entropy, 22.","DOI":"10.3390\/e22091002"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"113360","DOI":"10.1016\/j.enconman.2020.113360","article-title":"Performance evaluation and parametric optimum design of irreversible thermionic generators based on van der Waals heterostructures","volume":"225","author":"Qiu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"110656","DOI":"10.1016\/j.rser.2020.110656","article-title":"Finite-time thermodynamics modeling and analysis on compressed air energy storage systems with thermal storage","volume":"138","author":"Guo","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1515\/jnet-2020-0039","article-title":"Endoreversible Otto engines at maximal power","volume":"45","author":"Smith","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"113001","DOI":"10.1016\/j.enconman.2020.113001","article-title":"Power and efficiency optimization of open Maisotsenko-Brayton cycle and performance comparison with traditional open regenerated Brayton cycle","volume":"217","author":"Chen","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"113069","DOI":"10.1016\/j.enconman.2020.113069","article-title":"Analysis of integration method in multi-heat-source power generation systems based on finite-time thermodynamics","volume":"220","author":"Liu","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"112424","DOI":"10.1016\/j.enconman.2019.112424","article-title":"Power output, thermal efficiency and exergy-based ecological performance optimizations of an irreversible KCS-34 coupled to variable temperature heat reservoirs","volume":"205","author":"Feng","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2640","DOI":"10.1007\/s11431-019-1518-x","article-title":"Performance optimization of a class of combined thermoelectric heating devices","volume":"63","author":"Chen","year":"2020","journal-title":"Sci. China Technol. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1140\/epjp\/s13360-021-01162-z","article-title":"Ecological optimization of an irreversible Diesel cycle","volume":"136","author":"Ge","year":"2021","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"113585","DOI":"10.1016\/j.enconman.2020.113585","article-title":"Constructal thermodynamic optimization for dual-pressure organic Rankine cycle in waste heat utilization system","volume":"227","author":"Feng","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, R.B., Ge, Y.L., Chen, L.G., Feng, H.J., and Wu, Z.X. (2021). Power and thermal efficiency optimization of an irreversible steady flow Lenoir cycle. Entropy, 23.","DOI":"10.3390\/e23040425"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1515\/jnet-2020-0050","article-title":"Performance optimization for a multielement thermoelectric refrigerator with another linear heat transfer law","volume":"46","author":"Chen","year":"2021","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Berry, R.S., Salamon, P., and Andresen, B. (2020). How it all began. Entropy, 22.","DOI":"10.3390\/e22080908"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1063\/1.331592","article-title":"Optimal staging of endoreversible heat engines","volume":"53","author":"Rubin","year":"1982","journal-title":"J. Appl. Phys."},{"key":"ref_39","first-page":"289","article-title":"Analysis of finite time thermodynamics on a combined power cycle","volume":"3","author":"Chen","year":"1988","journal-title":"J. Xiamen Univ. (Nat. Sci.)"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0196-8904(90)90008-M","article-title":"Power performance of a cascade endoreversible cycle","volume":"30","author":"Wu","year":"1990","journal-title":"Energy Convers. Manag."},{"key":"ref_41","first-page":"41","article-title":"The optimal power performance of an endo-reversible combined cycle","volume":"65","author":"Wu","year":"1992","journal-title":"J. Inst. Energy"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3383","DOI":"10.1088\/0305-4470\/31\/15\/005","article-title":"A universal model of an irreversible combined Carnot cycle system and its general performance characteristics","volume":"31","author":"Chen","year":"1998","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2024","DOI":"10.1088\/0022-3727\/28\/10\/005","article-title":"The theoretical efficiency limits for a combined cycle under the condition of maximum power output","volume":"28","author":"Ozkaynak","year":"1995","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1016\/0360-5442(95)00076-S","article-title":"Steady-state thermodynamic analysis of a combined Carnot cycle with internal irreversibility","volume":"20","author":"Kodal","year":"1995","journal-title":"Energy"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1009648000309","article-title":"Andresen, B. Analysis of combined systems of two endoreversible engines","volume":"4","author":"Chen","year":"1997","journal-title":"Open Syst. Inf. Dyn."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1177\/030641909702500404","article-title":"Finite-Time Thermodynamic Analysis of Combined Heat Engines","volume":"25","author":"Assad","year":"1997","journal-title":"Int. J. Mech. Eng. Educ."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"91","DOI":"10.7227\/IJMEE.27.2.1","article-title":"Optimizing cascades of endo-reversible heat engines","volume":"27","author":"Lewins","year":"1999","journal-title":"Int. J. Mech. Eng. Educ."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"60510","DOI":"10.1088\/1674-1056\/24\/6\/060510","article-title":"Optimization of combined endoreversible Carnot heat engines with different objectives","volume":"24","author":"Cheng","year":"2015","journal-title":"Chin. Phys. B"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.ijheatmasstransfer.2015.07.077","article-title":"A new approach to determining the intermediate temperatures of endoreversible combined cycle power plant corresponding to maximum power","volume":"91","author":"Wu","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"50004","DOI":"10.1209\/0295-5075\/128\/50004","article-title":"Efficiency of a two-stage heat engine at optimal power","volume":"128","author":"Iyyappan","year":"2019","journal-title":"EPL"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1140\/epjb\/e2004-00140-y","article-title":"Current, maximum power and optimized efficiency of a Brownian heat engine","volume":"38","author":"Asfaw","year":"2004","journal-title":"Eur. Phys. J. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"062103","DOI":"10.1103\/PhysRevE.95.062103","article-title":"Performance optimization in two-dimensional Brownian rotary ratchet models","volume":"95","author":"Tutu","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"4658","DOI":"10.1016\/j.energy.2010.09.039","article-title":"Micro-\/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristics","volume":"35","author":"Nie","year":"2010","journal-title":"Energy"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"054903","DOI":"10.1063\/1.3072709","article-title":"Quantum boundary effect on the work output of a micro-\/nanoscaled Carnot cycle","volume":"105","author":"Nie","year":"2009","journal-title":"J. Appl. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1063\/1.446862","article-title":"A quantum mechanical open system as a model of a heat engine","volume":"80","author":"Kosloff","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"4398","DOI":"10.1063\/1.463909","article-title":"On the classical limit of quantum thermodynamics in finite time","volume":"97","author":"Geva","year":"1992","journal-title":"J. Chem. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"3054","DOI":"10.1063\/1.461951","article-title":"A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1\/2 systems as the working fluid","volume":"96","author":"Geva","year":"1992","journal-title":"J. Chem. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1088\/0022-3727\/32\/6\/011","article-title":"On the power cycles working with ideal quantum gases: I. The Ericsson cycle","volume":"32","author":"Sisman","year":"1999","journal-title":"J. Phys. D: Appl. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/S0306-2619(00)00063-5","article-title":"The improvement effect of quantum degeneracy on the work from a Carnot cycle","volume":"68","author":"Saygin","year":"2001","journal-title":"Appl. Energy"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"3086","DOI":"10.1063\/1.1396831","article-title":"Quantum degeneracy effect on the work output from a Stirling cycle","volume":"90","year":"2001","journal-title":"J. Appl. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1238\/Physica.Regular.064a00108","article-title":"Re-Optimisation of Otto Power Cycles Working with Ideal Quantum Gases","volume":"64","author":"Sisman","year":"2001","journal-title":"Phys. Scr."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1023\/B:OPSY.0000024759.64343.aa","article-title":"The influence of quantum degeneracy on the performance of a Fermi Brayton engine","volume":"11","author":"Lin","year":"2004","journal-title":"Open Syst. Inf. Dyn."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"083534","DOI":"10.1063\/1.3103315","article-title":"Performance analysis and parametric optimum criteria of an irreversible Bose-Otto engine","volume":"105","author":"Wang","year":"2009","journal-title":"J. Appl. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"010505","DOI":"10.1088\/1674-1056\/21\/1\/010505","article-title":"Optimization criteria of a Bose Brayton heat engine","volume":"21","author":"Wang","year":"2012","journal-title":"Chin. Phys. B"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1016\/j.applthermaleng.2008.03.042","article-title":"Performance analysis and parametric optimum criteria of a quantum Otto heat engine with heat transfer effects","volume":"29","author":"Wang","year":"2009","journal-title":"Appl. Therm. Eng."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1990","DOI":"10.1016\/j.physleta.2015.06.020","article-title":"Application of exergetic sustainability index to a nano-scale irreversible Brayton cycle operating with ideal Bose and Fermi gasses","volume":"379","author":"Caner","year":"2015","journal-title":"Phys. Lett. A"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.physa.2015.03.064","article-title":"Determining of the optimum performance of a nano scale irreversible Dual cycle with quantum gases as working fluid by using different methods","volume":"433","author":"Caner","year":"2015","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"4427","DOI":"10.1088\/0305-4470\/33\/24\/302","article-title":"Quantum mechanical Carnot engine","volume":"33","author":"Bender","year":"2000","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"041117","DOI":"10.1103\/PhysRevE.83.041117","article-title":"Maximum-power quantum-mechanical Carnot engine","volume":"83","author":"Abe","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"124140","DOI":"10.1016\/j.physa.2020.124140","article-title":"Power and efficiency optimization of an irreversible quantum Carnot heat engine working with harmonic oscillators","volume":"550","author":"Chen","year":"2020","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"062119","DOI":"10.1103\/PhysRevE.98.062119","article-title":"Bose-Fermi duality in a quantum Otto heat engine with trapped repulsive bosons","volume":"98","author":"Chen","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Kosloff, R., and Rezek, Y. (2017). The quantum harmonic otto cycle. Entropy, 19.","DOI":"10.3390\/e19040136"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"40001","DOI":"10.1209\/0295-5075\/108\/40001","article-title":"Universal features in the efficiency at maximal work of hot quantum Otto engines","volume":"108","author":"Uzdin","year":"2014","journal-title":"EPL"},{"key":"ref_74","doi-asserted-by":"crossref","unstructured":"Insinga, A.R. (2020). The Quantum Friction and Optimal Finite-Time Performance of the Quantum Otto Cycle. Entropy, 22.","DOI":"10.3390\/e22091060"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"062153","DOI":"10.1103\/PhysRevE.97.062153","article-title":"Quantum heat engines: Limit cycles and exceptional points","volume":"97","author":"Insinga","year":"2018","journal-title":"Phys. Rev. E"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"046105","DOI":"10.1103\/PhysRevE.67.046105","article-title":"Performance analysis of an irreversible quantum heat engine working with harmonic oscillators","volume":"67","author":"Lin","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"2100","DOI":"10.3390\/e15062100","article-title":"Quantum thermodynamics: A dynamical viewpoint","volume":"15","author":"Kosloff","year":"2013","journal-title":"Entropy"},{"key":"ref_78","first-page":"1","article-title":"Chapter 1. Introduction to Quantum Thermodynamics: History and Prospects","volume":"Volume 195","author":"Binder","year":"2018","journal-title":"Thermodynamics in the Quantum Regime, Fundamental Theories of Physics"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1146\/annurev-physchem-040513-103724","article-title":"Quantum heat engines and refrigerators: Continuous devices","volume":"65","author":"Kosloff","year":"2014","journal-title":"Annu. Rev. Phys. Chem."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"40004","DOI":"10.1209\/0295-5075\/109\/40004","article-title":"Finite-time availability in a quantum system","volume":"109","author":"Hoffmann","year":"2015","journal-title":"EPL"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1515\/jnet-2015-0025","article-title":"Quantum finite time availability for parametric oscillators","volume":"40","author":"Hoffmann","year":"2015","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_82","first-page":"204105","article-title":"Quantum finite-time availability","volume":"150","author":"Kosloff","year":"2019","journal-title":"Atti della Accad. Peloritana dei Pericolanti"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"204105","DOI":"10.1063\/1.5096173","article-title":"Quantum thermodynamics and open-systems modeling","volume":"150","author":"Kosloff","year":"2019","journal-title":"J. Chem. Phys."},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Dann, R., Kosloff, R., and Salamon, P. (2020). Quantum finite time thermodynamics: Insight from a single qubit engine. Entropy, 22.","DOI":"10.3390\/e22111255"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"122597","DOI":"10.1016\/j.physa.2019.122597","article-title":"Exergy-based ecological optimization of an irreversible quantum Carnot heat pump with harmonic oscillators","volume":"537","author":"Chen","year":"2020","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"011007","DOI":"10.1115\/1.4043186","article-title":"Optimal ecological performance investigation of a quantum harmonic oscillator Brayton refrigerator","volume":"12","author":"Liu","year":"2020","journal-title":"Trans. ASME, J. Thermal Sci. Eng. Appl."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"13055","DOI":"10.1088\/1367-2630\/ab6876","article-title":"Quantum signatures in the quantum Carnot cycle","volume":"22","author":"Dann","year":"2020","journal-title":"New J. Phys."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1515\/jnet-2020-0028","article-title":"Exergy-based ecological optimization of an irreversible quantum Carnot heat pump with spin-1\/2 systems","volume":"46","author":"Liu","year":"2021","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1126\/science.aad6320","article-title":"A single-atom heat engine","volume":"352","author":"Dawkins","year":"2016","journal-title":"Science"},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"63019","DOI":"10.1088\/1367-2630\/ab2684","article-title":"Ultra-cold single-atom quantum heat engines","volume":"21","author":"Barontini","year":"2019","journal-title":"New J. Phys."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"240601","DOI":"10.1103\/PhysRevLett.123.240601","article-title":"Experimental characterization of a spin quantum heat engine","volume":"123","author":"Peterson","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"170601","DOI":"10.1103\/PhysRevLett.120.170601","article-title":"Single-atom heat machines enabled by energy quantization","volume":"120","author":"Bylinskii","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Meng, Z.W., Chen, L.G., and Wu, F. (2020). Optimal power and efficiency of multi-stage endoreversible quantum Carnot heat engine with harmonic oscillators at the classical limit. Entropy, 22.","DOI":"10.3390\/e22040457"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Qi, C.Z., Ding, Z.M., Chen, L.G., Ge, Y.L., and Feng, H.J. (2021). Modeling and performance optimization of an irreversible two-stage combined thermal Brownian heat engine. Entropy, 23.","DOI":"10.3390\/e23040419"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1515\/jnet-2020-0084","article-title":"Modelling of irreversible two-stage combined thermal Brownian refrigerators and their optimal performance","volume":"46","author":"Qi","year":"2021","journal-title":"J. Non-Equilibr. Thermodyn."},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Schwabl, F. (2002). Ideal Quantum Gases. Statistical Mechanics, Springer. Advanced Texts in Physics.","DOI":"10.1007\/978-3-662-04702-6"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"055005","DOI":"10.1088\/0031-8949\/77\/05\/055005","article-title":"Optimum performance analysis of an irreversible quantum cryogenic refrigeration cycle working with an ideal Bose or Fermi gas","volume":"77","author":"Lin","year":"2008","journal-title":"Phys. Scr."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/5\/536\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:53:28Z","timestamp":1760162008000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/5\/536"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,27]]},"references-count":97,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["e23050536"],"URL":"https:\/\/doi.org\/10.3390\/e23050536","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,4,27]]}}}