Abstract models for heat engines
Zhan-Chun Tu
Abstract models for heat engines
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.
abstract model / heat engine / finite-time thermodynamics
[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)
CrossRef
ADS
Google scholar
|
[3] |
F. L. Curzon and B. Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys. 43(1), 22 (1975)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[6] |
A. De Vos, Efficiency of some heat engines at maximumpower conditions, Am. J. Phys. 53(6), 570 (1985)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[9] |
A. Bejan, Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes, J. Appl. Phys. 79(3), 1191 (1996)
CrossRef
ADS
Google scholar
|
[10] |
C. Van den Broeck, Thermodynamic efficiency at maximum power, Phys. Rev. Lett. 95(19), 190602 (2005)
CrossRef
ADS
Google scholar
|
[11] |
B. Jiménez de Cisneros and A. C. Hernández, Collective working regimes for coupled heat engines, Phys. Rev. Lett. 98(13), 130602 (2007)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[14] |
B. Gaveau, M. Moreau, and L. S. Schulman, Stochastic thermodynamics and sustainable efficiency in work production, Phys. Rev. Lett. 105(6), 060601 (2010)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[21] |
Y. Izumida and K. Okuda, Efficiency at maximum power of minimally nonlinear irreversible heat engines, Europhys. Lett. 97(1), 10004 (2012)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[27] |
Y. Izumida and K. Okuda, Linear irreversible heat engines based on local equilibrium assumptions, New J. Phys. 17(8), 085011 (2015)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[31] |
Y. Apertet, H. Ouerdane, C. Goupil, and Ph. Lecoeur, True nature of the Curzon–Ahlborn efficiency, Phys. Rev. E 96(2), 022119 (2017)
CrossRef
ADS
Google scholar
|
[32] |
H. Wang, J. He, and J. Wang, Endoreversible quantum heat engines in the linear response regime, Phys. Rev. E 96(1), 012152 (2017)
CrossRef
ADS
Google scholar
|
[33] |
S. H. Lee, J. Um, and H. Park, Nonuniversality of heatengine efficiency at maximum power, Phys. Rev. E 98(5), 052137 (2018)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[36] |
V. Blickle and C. Bechinger, Realization of a micrometresized stochastic heat engine, Nat. Phys. 8(2), 143 (2012)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[40] |
T. Schmiedl and U. Seifert, Efficiency at maximum power: An analytically solvable model for stochastic heat engines, Europhys. Lett. 81(2), 20003 (2008)
CrossRef
ADS
Google scholar
|
[41] |
Z. C. Tu, Efficiency at maximum power of Feynman’s ratchet as a heat engine, J. Phys. A 41(31), 312003 (2008)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[43] |
M. Esposito, K. Lindenberg, and C. Van den Broeck, Universality of efficiency at maximum power, Phys. Rev. Lett. 102(13), 130602 (2009)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[45] |
U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75(12), 126001 (2012)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[48] |
L. Onsager, Reciprocal Relations in Irreversible Processes. I., Phys. Rev. 37(4), 405 (1931)
CrossRef
ADS
Google scholar
|
[49] |
H. B. G. Casimir, On Onsager’s Principle of Microscopic Reversibility, Rev. Mod. Phys. 17(2–3), 343 (1945)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[52] |
R. Landauer, Motion out of noisy states, J. Stat. Phys. 53(1–2), 233 (1988)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[55] |
G. Verley, M. Esposito, T. Willaert, and C. Van den Broeck, The unlikely Carnot efficiency, Nat. Commun. 5(1), 4721 (2014)
CrossRef
ADS
Google scholar
|
[56] |
G. Verley, T. Willaert, C. Van den Broeck, and M. Esposito, Universal theory of efficiency fluctuations,Phys. Rev. E 90(5), 052145 (2014)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[59] |
T. Denzler and E. Lutz, Efficiency fluctuations of a quantum heat engine, Phys. Rev. Research 2, 032062 (2020)
CrossRef
ADS
Google scholar
|
[60] |
A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114(15), 158101 (2015)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[62] |
V. Holubec and A. Ryabov, Maximum efficiency of lowdissipation heat engines at arbitrary power, J. Stat. Mech. 2016(7), 073204 (2016)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[64] |
A. Ryabov and V. Holubec, Maximum efficiency of steadystate heat engines at arbitrary power, Phys. Rev. E 93, 050101(R) (2016)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[66] |
K. Proesmans, B. Cleuren, and C. Van den Broeck, Powerefficiency- dissipation relations in linear thermodynamics, Phys. Rev. Lett. 116(22), 220601 (2016)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[69] |
A. Emmanouilidou, X. G. Zhao, P. Ao, and Q. Niu, Steering an eigenstate to a destination, Phys. Rev. Lett. 85(8), 1626 (2000)
CrossRef
ADS
Google scholar
|
[70] |
M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107(46), 9937 (2003)
CrossRef
ADS
Google scholar
|
[71] |
M. V. Berry, Transitionless quantum driving, J. Phys. A 42(36), 365303 (2009)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[73] |
C. Jarzynski, Generating shortcuts to adiabaticity in quantum and classical dynamics, Phys. Rev. A 88, 040101(R) (2013)
CrossRef
ADS
Google scholar
|
[74] |
A. del Campo, Shortcuts to adiabaticity by counterdiabatic driving, Phys. Rev. Lett. 111(10), 100502 (2013)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[78] |
Z. C. Tu, Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity, Phys. Rev. E 89(5), 052148 (2014)
CrossRef
ADS
Google scholar
|
[79] |
O. Abah and E. Lutz, Performance of shortcut-toadiabaticity quantum engines, Phys. Rev. E 98(3), 032121 (2018)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[81] |
G. Li, H. T. Quan, and Z. C. Tu, Shortcuts to isothermality and nonequilibrium work relations, Phys. Rev. E 96(1), 012144 (2017)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[85] |
K. Nakamura, J. Matrasulov, and Y. Izumida, Fastforward approach to stochastic heat engine, Phys. Rev. E 102(1), 012129 (2020)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[92] |
I. A. Martínez, É. Roldán, L. Dinis, and R. A. Rica, Colloidal heat engines: A review, Soft Matter 13(1), 22 (2017)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[94] |
T. Ekeh, M. Cates, and É. Fodor, Thermodynamic cycles with active matter, Phys. Rev. E 102, 010101(R) (2020)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[96] |
J. S. Lee, J. M. Park, and H. Park, Brownian heat engine with active reservoirs, Phys. Rev. E 102(3), 032116 (2020)
CrossRef
ADS
Google scholar
|
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