Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2021, Vol. 16 Issue (3) : 33202    https://doi.org/10.1007/s11467-020-1029-6
TOPICAL REVIEW
Abstract models for heat engines
Zhan-Chun Tu()
Department of Physics, Beijing Normal University, Beijing 100875, China
 Download: PDF(1005 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

We retrospect three abstract models for heat engines which include a classic abstract model in textbook of thermal physics, a primary abstract model for finite-time heat engines, and a refined abstract model for finite-time heat engines. The detailed models of heat engines in literature of finite-time thermodynamics may be mapped into the refined abstract model. The future developments based on the refined abstract model are also surveyed.

Keywords abstract model      heat engine      finite-time thermodynamics     
Corresponding Author(s): Zhan-Chun Tu   
Issue Date: 18 December 2020
 Cite this article:   
Zhan-Chun Tu. Abstract models for heat engines[J]. Front. Phys. , 2021, 16(3): 33202.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-020-1029-6
https://academic.hep.com.cn/fop/EN/Y2021/V16/I3/33202
1 P. Chambadal, Les Centrales Nuclaires, Armand Colin, Paris, 1957
2 I. I. Novikov, Efficiency of an atomic power generating installation, Soviet J. Atomic Energy 3, 1269 (1957)
https://doi.org/10.1007/BF01507240
3 F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43(1), 22 (1975)
https://doi.org/10.1119/1.10023
4 B. Andresen, P. Salamon, and R. S. Berry, Thermodynamics in finite time: Extremals for imperfect heat engines, J. Chem. Phys. 66(4), 1571 (1977)
https://doi.org/10.1063/1.434122
5 K. H. Hoffmann, S. J. Watowich, and R. S. Berry, Optimal paths for thermodynamic systems: The ideal Diesel cycle, J. Appl. Phys. 58(6), 2125 (1985)
https://doi.org/10.1063/1.335977
6 A. De Vos, Efficiency of some heat engines at maximumpower conditions, Am. J. Phys. 53(6), 570 (1985)
https://doi.org/10.1119/1.14240
7 L. Chen and Z. Yan, The effect of heat-transfer law on performance of a two-heat-source endoreversible cycle, J. Chem. Phys. 90(7), 3740 (1989)
https://doi.org/10.1063/1.455832
8 J. Chen, The maximum power output and maximum efficiency of an irreversible Carnot heat engine, J. Phys. D Appl. Phys. 27(6), 1144 (1994)
https://doi.org/10.1088/0022-3727/27/6/011
9 A. Bejan, Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes, J. Appl. Phys. 79(3), 1191 (1996)
https://doi.org/10.1063/1.362674
10 C. Van den Broeck, Thermodynamic efficiency at maximum power, Phys. Rev. Lett. 95(19), 190602 (2005)
https://doi.org/10.1103/PhysRevLett.95.190602
11 B. Jiménez de Cisneros and A. C. Hernández, Collective working regimes for coupled heat engines, Phys. Rev. Lett. 98(13), 130602 (2007)
https://doi.org/10.1103/PhysRevLett.98.130602
12 M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Efficiency at maximum power of low-dissipation Carnot engines, Phys. Rev. Lett. 105(15), 150603 (2010)
https://doi.org/10.1103/PhysRevLett.105.150603
13 M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Quantum-dot Carnot engine at maximum power, Phys. Rev. E 81(4), 041106 (2010)
https://doi.org/10.1103/PhysRevE.81.041106
14 B. Gaveau, M. Moreau, and L. S. Schulman, Stochastic thermodynamics and sustainable efficiency in work production, Phys. Rev. Lett. 105(6), 060601 (2010)
https://doi.org/10.1103/PhysRevLett.105.060601
15 L. Chen, Z. Ding, and F. Sun, Optimum performance analysis of Feynman’s engine as cold and hot ratchets, J. Non- Equilib. Thermodyn. 36(2), 155 (2011)
https://doi.org/10.1515/jnetdy.2011.011
16 Y. Wang and Z. C. Tu, Efficiency at maximum power output of linear irreversible Carnot-like heat engines, Phys. Rev. E 85(1), 011127 (2012)
https://doi.org/10.1103/PhysRevE.85.011127
17 Y. Wang and Z. C. Tu, Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines, Europhys. Lett. 98(4), 40001 (2012)
https://doi.org/10.1209/0295-5075/98/40001
18 Y. Wang and Z. C. Tu, Bounds of efficiency at maximum power for normal-, sub- and superdissipative Carnot-like heat engines, Commum. Theor. Phys. 59(2), 175 (2013)
https://doi.org/10.1088/0253-6102/59/2/08
19 J. Wang and J. He, Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction, Phys. Rev. E 86(5), 051112 (2012)
https://doi.org/10.1103/PhysRevE.86.051112
20 Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, Irreversibilities and efficiency at maximum power of heat engines: The illustrative case of a thermoelectric generator, Phys. Rev. E 85(3), 031116 (2012)
https://doi.org/10.1103/PhysRevE.85.031116
21 Y. Izumida and K. Okuda, Efficiency at maximum power of minimally nonlinear irreversible heat engines, Europhys. Lett. 97(1), 10004 (2012)
https://doi.org/10.1209/0295-5075/97/10004
22 J. Guo, J. Wang, Y. Wang, and J. Chen, Universal efficiency bounds of weak-dissipative thermodynamic cycles at the maximum power output, Phys. Rev. E 87(1), 012133 (2013)
https://doi.org/10.1103/PhysRevE.87.012133
23 Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, From local force-flux relationships to internal dissipations and their impact on heat engine performance: The illustrative case of a thermoelectric generator, Phys. Rev. E 88(2), 022137 (2013)
https://doi.org/10.1103/PhysRevE.88.022137
24 J. Gonzalez-Ayala, L. A. Arias-Hernandez, and F. Angulo-Brown, Connection between maximum-work and maximum-power thermal cycles, Phys. Rev. E 88(5), 052142 (2013)
https://doi.org/10.1103/PhysRevE.88.052142
25 H. T. Quan, Maximum efficiency of ideal heat engines based on a small system: Correction to the Carnot efficiency at the nanoscale, Phys. Rev. E 89(6), 062134 (2014)
https://doi.org/10.1103/PhysRevE.89.062134
26 A. Calvo Hernández, J. M. M. Roco, A. Medina, S. Velasco, and L. Guzmán-Vargas, The maximum power efficiency 1−τ: Research, education, and bibliometric relevance, Eur. Phys. J. Spec. Top. 224(5), 809 (2015)
https://doi.org/10.1140/epjst/e2015-02429-4
27 Y. Izumida and K. Okuda, Linear irreversible heat engines based on local equilibrium assumptions, New J. Phys. 17(8), 085011 (2015)
https://doi.org/10.1088/1367-2630/17/8/085011
28 R. Long and W. Liu, Efficiency and its bounds of minimally nonlinear irreversible heat engines at arbitrary power, Phys. Rev. E 94(5), 052114 (2016)
https://doi.org/10.1103/PhysRevE.94.052114
29 J. Koning, and J. Indekeu, Engines with ideal efficiency and nonzero power for sublinear transport laws, Eur. Phys. J. B 89(11), 248 (2016)
https://doi.org/10.1140/epjb/e2016-70297-9
30 Y. Yu, Z. Ding, L. Chen, W. Wang, and F. Sun, Power and efficiency optimization for an energy selective electron heat engine with double-resonance energy filter, Energy 107, 287 (2016)
https://doi.org/10.1016/j.energy.2016.04.006
31 Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, True nature of the Curzon–Ahlborn efficiency, Phys. Rev. E 96(2), 022119 (2017)
https://doi.org/10.1103/PhysRevE.96.022119
32 H. Wang, J. He, and J. Wang, Endoreversible quantum heat engines in the linear response regime, Phys. Rev. E 96(1), 012152 (2017)
https://doi.org/10.1103/PhysRevE.96.012152
33 S. H. Lee, J. Um, and H. Park, Nonuniversality of heatengine efficiency at maximum power, Phys. Rev. E 98(5), 052137 (2018)
https://doi.org/10.1103/PhysRevE.98.052137
34 Y. H. Ma, D. Xu, H. Dong, and C. P. Sun, Optimal operating protocol to achieve efficiency at maximum power of heat engines, Phys. Rev. E 98(2), 022133 (2018)
https://doi.org/10.1103/PhysRevE.98.022133
35 J. Gonzalez-Ayala, J. Guo, A. Medina, J. M. M. Roco, and A. C. Hernández, Energetic self-optimization induced by stability in low-dissipation heat engines, Phys. Rev. Lett. 124(5), 050603 (2020)
https://doi.org/10.1103/PhysRevLett.124.050603
36 V. Blickle and C. Bechinger, Realization of a micrometresized stochastic heat engine, Nat. Phys. 8(2), 143 (2012)
https://doi.org/10.1038/nphys2163
37 I. A. Martínez, É. Roldán, L. Dinis, D. Petrov, J. M. R. Parrondo, and R. A. Rica, Brownian Carnot engine, Nat. Phys. 12(1), 67 (2016)
https://doi.org/10.1038/nphys3518
38 S. Deng, A. Chenu, P. Diao, F. Li, S. Yu, I. Coulamy, A. del Campo, and H. Wu, Superadiabatic quantum friction suppression in finite-time thermodynamics, Sci. Adv. 4(4), eaar5909 (2018)
https://doi.org/10.1126/sciadv.aar5909
39 Y. H. Ma, R. X. Zhai, C. P. Sun, and H. Dong, Experimental validation of the 1/τ -scaling entropy generation in finite-time thermodynamics with dry air, Phys. Rev. Lett. 125(21), 210601 (2020)
https://doi.org/10.1103/PhysRevLett.125.210601
40 T. Schmiedl and U. Seifert, Efficiency at maximum power: An analytically solvable model for stochastic heat engines, Europhys. Lett. 81(2), 20003 (2008)
https://doi.org/10.1209/0295-5075/81/20003
41 Z. C. Tu, Efficiency at maximum power of Feynman’s ratchet as a heat engine, J. Phys. A 41(31), 312003 (2008)
https://doi.org/10.1088/1751-8113/41/31/312003
42 M. Esposito, K. Lindenberg, and C. Van den Broeck, Thermoelectric efficiency at maximum power in a quantum dot, Europhys. Lett. 85(6), 60010 (2009)
https://doi.org/10.1209/0295-5075/85/60010
43 M. Esposito, K. Lindenberg, and C. Van den Broeck, Universality of efficiency at maximum power, Phys. Rev. Lett. 102(13), 130602 (2009)
https://doi.org/10.1103/PhysRevLett.102.130602
44 S. Q. Sheng and Z. C. Tu, Universality of energy conversion efficiency for optimal tightcoupling heat engines and refrigerators, J. Phys. A 46(40), 402001 (2013)
https://doi.org/10.1088/1751-8113/46/40/402001
45 U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75(12), 126001 (2012)
https://doi.org/10.1088/0034-4885/75/12/126001
46 S. Q. Sheng and Z. C. Tu, Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics, Phys. Rev. E 89(1), 012129 (2014)
https://doi.org/10.1103/PhysRevE.89.012129
47 S. Q. Sheng and Z. C. Tu, Constitutive relation for nonlinear response and universality of efficiency at maximum power for tight-coupling heat engines, Phys. Rev. E 91(2), 022136 (2015)
https://doi.org/10.1103/PhysRevE.91.022136
48 L. Onsager, Reciprocal Relations in Irreversible Processes. I., Phys. Rev. 37(4), 405 (1931)
https://doi.org/10.1103/PhysRev.37.405
49 H. B. G. Casimir, On Onsager’s Principle of Microscopic Reversibility, Rev. Mod. Phys. 17(2–3), 343 (1945)
https://doi.org/10.1103/RevModPhys.17.343
50 I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, 3rd Ed., Interscience, New York, 1961
51 M. Büttiker, Transport as a consequence of statedependent diffusion, Z. Phys. B 68(2–3), 161 (1987)
https://doi.org/10.1007/BF01304221
52 R. Landauer, Motion out of noisy states, J. Stat. Phys. 53(1–2), 233 (1988)
https://doi.org/10.1007/BF01011555
53 S. Q. Sheng and Z. C. Tu, Hidden symmetries and nonlinear constitutive relations for tightcoupling heat engines, New J. Phys. 17(4), 045013 (2015)
https://doi.org/10.1088/1367-2630/17/4/045013
54 O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer, and E. Lutz, Singleion heat engine at maximum power, Phys. Rev. Lett. 109(20), 203006 (2012)
https://doi.org/10.1103/PhysRevLett.109.203006
55 G. Verley, M. Esposito, T. Willaert, and C. Van den Broeck, The unlikely Carnot efficiency, Nat. Commun. 5(1), 4721 (2014)
https://doi.org/10.1038/ncomms5721
56 G. Verley, T. Willaert, C. Van den Broeck, and M. Esposito, Universal theory of efficiency fluctuations,Phys. Rev. E 90(5), 052145 (2014)
https://doi.org/10.1103/PhysRevE.90.052145
57 J. H. Jiang, B. K. Agarwalla, and D. Segal, Efficiency statistics and bounds for systems with broken timereversal symmetry, Phys. Rev. Lett. 115(4), 040601 (2015)
https://doi.org/10.1103/PhysRevLett.115.040601
58 J. M. Park, H. M. Chun, and J. D. Noh, Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat-engine model, Phys. Rev. E 94(1), 012127 (2016)
https://doi.org/10.1103/PhysRevE.94.012127
59 T. Denzler and E. Lutz, Efficiency fluctuations of a quantum heat engine, Phys. Rev. Research 2, 032062 (2020)
https://doi.org/10.1103/PhysRevResearch.2.032062
60 A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114(15), 158101 (2015)
https://doi.org/10.1103/PhysRevLett.114.158101
61 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(5), 050601 (2013)
https://doi.org/10.1103/PhysRevLett.111.050601
62 V. Holubec and A. Ryabov, Maximum efficiency of lowdissipation heat engines at arbitrary power, J. Stat. Mech. 2016(7), 073204 (2016)
https://doi.org/10.1088/1742-5468/2016/07/073204
63 Y. H. Ma, D. Xu, H. Dong, and C. P. Sun, Universal constraint for efficiency and power of a low-dissipation heat engine, Phys. Rev. E 98(4), 042112 (2018)
https://doi.org/10.1103/PhysRevE.98.042112
64 A. Ryabov and V. Holubec, Maximum efficiency of steadystate heat engines at arbitrary power, Phys. Rev. E 93, 050101(R) (2016)
https://doi.org/10.1103/PhysRevE.93.050101
65 I. Iyyappan and M. Ponmurugan, General relations between the power, efficiency, and dissipation for the irreversible heat engines in the nonlinear response regime, Phys. Rev. E 97(1), 012141 (2018)
https://doi.org/10.1103/PhysRevE.97.012141
66 K. Proesmans, B. Cleuren, and C. Van den Broeck, Powerefficiency- dissipation relations in linear thermodynamics, Phys. Rev. Lett. 116(22), 220601 (2016)
https://doi.org/10.1103/PhysRevLett.116.220601
67 N. Shiraishi, K. Saito, and H. Tasaki, Universal tradeoff relation between power and efficiency for heat engines, Phys. Rev. Lett. 117(19), 190601 (2016)
https://doi.org/10.1103/PhysRevLett.117.190601
68 P. Pietzonka and U. Seifert, Universal trade-off between power, efficiency, and constancy in steady-state heat engines, Phys. Rev. Lett. 120(19), 190602 (2018)
https://doi.org/10.1103/PhysRevLett.120.190602
69 A. Emmanouilidou, X. G. Zhao, P. Ao, and Q. Niu, Steering an eigenstate to a destination, Phys. Rev. Lett. 85(8), 1626 (2000)
https://doi.org/10.1103/PhysRevLett.85.1626
70 M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107(46), 9937 (2003)
https://doi.org/10.1021/jp030708a
71 M. V. Berry, Transitionless quantum driving, J. Phys. A 42(36), 365303 (2009)
https://doi.org/10.1088/1751-8113/42/36/365303
72 X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Fast optimal frictionless atom cooling in harmonic traps: Shortcut to adiabaticity, Phys. Rev. Lett. 104(6), 063002 (2010)
https://doi.org/10.1103/PhysRevLett.104.063002
73 C. Jarzynski, Generating shortcuts to adiabaticity in quantum and classical dynamics, Phys. Rev. A 88, 040101(R) (2013)
https://doi.org/10.1103/PhysRevA.88.040101
74 A. del Campo, Shortcuts to adiabaticity by counterdiabatic driving, Phys. Rev. Lett. 111(10), 100502 (2013)
https://doi.org/10.1103/PhysRevLett.111.100502
75 S. Deffner, C. Jarzynski, and A. del Campo, Classical and quantum shortcuts to adiabaticity for scale-invariant driving, Phys. Rev. X 4(2), 021013 (2014)
https://doi.org/10.1103/PhysRevX.4.021013
76 D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91(4), 045001 (2019)
https://doi.org/10.1103/RevModPhys.91.045001
77 J. Deng, Q. Wang, Z. Liu, P. Hanggi, and J. Gong, Boosting work characteristics and overall heat-engine performance via shortcuts to adiabaticity: Quantum and classical systems, Phys. Rev. E 88(6), 062122 (2013)
https://doi.org/10.1103/PhysRevE.88.062122
78 Z. C. Tu, Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity, Phys. Rev. E 89(5), 052148 (2014)
https://doi.org/10.1103/PhysRevE.89.052148
79 O. Abah and E. Lutz, Performance of shortcut-toadiabaticity quantum engines, Phys. Rev. E 98(3), 032121 (2018)
https://doi.org/10.1103/PhysRevE.98.032121
80 C. Plata, D. Guéry-Odelin, E. Trizac, and A. Prados, Building an irreversible Carnot-like heat engine with an overdamped harmonic oscillator, J. Stat. Mech. 2020(9), 093207 (2020)
https://doi.org/10.1088/1742-5468/abb0e1
81 G. Li, H. T. Quan, and Z. C. Tu, Shortcuts to isothermality and nonequilibrium work relations, Phys. Rev. E 96(1), 012144 (2017)
https://doi.org/10.1103/PhysRevE.96.012144
82 J. A. C. Albay, S. R. Wulaningrum, C. Kwon, P. Y. Lai, and Y. Jun, Thermodynamic cost of a shortcuts-toisothermal transport of a Brownian particle, Phys. Rev. Research 1(3), 033122 (2019)
https://doi.org/10.1103/PhysRevResearch.1.033122
83 J. A. C. Albay, P. Y. Lai, and Y. Jun, Realization of finiterate isothermal compression and expansion using optical feedback trap, Appl. Phys. Lett. 116(10), 103706 (2020)
https://doi.org/10.1063/1.5143602
84 N. Pancotti, M. Scandi, M. T. Mitchison, and M. Perarnau-Llobet, Speed-ups to isothermality: Enhanced quantum thermal machines through control of the systembath coupling, Phys. Rev. X 10(3), 031015 (2020)
https://doi.org/10.1103/PhysRevX.10.031015
85 K. Nakamura, J. Matrasulov, and Y. Izumida, Fastforward approach to stochastic heat engine, Phys. Rev. E 102(1), 012129 (2020)
https://doi.org/10.1103/PhysRevE.102.012129
86 A. C. Hernández, A. Medina, J. M. M. Roco, J. A. White, and S. Velasco, Unified optimization criterion for energy converters, Phys. Rev. E 63(3), 037102 (2001)
https://doi.org/10.1103/PhysRevE.63.037102
87 N. Sánchez-Salas, L. López-Palacios, S. Velasco, and A. Calvo Hernández, Optimization criteria, bounds, and efficiencies of heat engines, Phys. Rev. E 82(5), 051101 (2010)
https://doi.org/10.1103/PhysRevE.82.051101
88 C. de Tomas, J. M. M. Roco, A. C. Hernández, Y. Wang, and Z. C. Tu, Low-dissipation heat devices: Unified tradeoff optimization and bounds, Phys. Rev. E 87(1), 012105 (2013)
https://doi.org/10.1103/PhysRevE.87.012105
89 Y. Zhang, C. Huang, G. Lin, and J. Chen, Universality of efficiency at unified trade-off optimization, Phys. Rev. E 93(3), 032152 (2016)
https://doi.org/10.1103/PhysRevE.93.032152
90 L. Zhao and Z. C. Tu, Nonlinear constitutive relation and efficiency at maximum power of non-homotypic heat engines, J. Beijing Normal Univ. (Natural Science) 52, 550 (2016)
91 S. Krishnamurthy, S. Ghosh, D. Chatterji, R. Ganapathy, and A. K. Sood, A micrometre-sized heat engine operating between bacterial reservoirs, Nat. Phys. 12(12), 1134 (2016)
https://doi.org/10.1038/nphys3870
92 I. A. Martínez, É. Roldán, L. Dinis, and R. A. Rica, Colloidal heat engines: A review, Soft Matter 13(1), 22 (2017)
https://doi.org/10.1039/C6SM00923A
93 P. Pietzonka, É. Fodor, C. Lohrmann, M. E. Cates, and U. Seifert, Autonomous engines driven by active Matter: Energetics and design principles, Phys. Rev. X 9(4), 041032 (2019)
https://doi.org/10.1103/PhysRevX.9.041032
94 T. Ekeh, M. Cates, and É. Fodor, Thermodynamic cycles with active matter, Phys. Rev. E 102, 010101(R) (2020)
https://doi.org/10.1103/PhysRevE.102.010101
95 A. Kumari, P. S. Pal, A. Saha, and S. Lahiri, Stochastic heat engine using an active particle, Phys. Rev. E 101(3), 032109 (2020)
https://doi.org/10.1103/PhysRevE.101.032109
96 J. S. Lee, J. M. Park, and H. Park, Brownian heat engine with active reservoirs, Phys. Rev. E 102(3), 032116 (2020)
https://doi.org/10.1103/PhysRevE.102.032116
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed