Abstract
The seminal work by Sadi Carnot in the early nineteenth century provided the blueprint of a reversible heat engine and the celebrated second law of thermodynamics eventually followed. Almost two centuries later, the quest to formulate a quantum theory of the thermodynamic laws has thus unsurprisingly motivated physicists to visualize what are known as ‘quantum thermal machines’ (QTMs). In this article, we review the prominent developments achieved in the theoretical construction as well as understanding of QTMs, beginning from the formulation of their earliest prototypes to recent models. We also present a detailed introduction and highlight recent progress in the rapidly developing field of ‘quantum batteries’.
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Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This review article does not discuss any new or previously published data. Appropriate permissions have been obtained for all the figures reused in this article from previous publications.]
References
M. Zemansky, R. Dittman, Heat and Thermodynamics, 7th edn. (McGraw Hill Education, New York, 1997)
J. Gemmer, M. Michel, G. Mahler, Quantum Thermodynamics (Springer, Berlin, 2010)
T. Jahnke, G. Mahler, Europhys. Lett. 90(5), 50008 (2010)
N. Linden, S. Popescu, P. Skrzypczyk, Phys. Rev. Lett. 105, 130401 (2010)
R. Kosloff, Entropy 15, 2100 (2013)
M. Horodecki, J. Oppenheim, Nat. Commun. 4, 2059 (2013)
S. Vinjanampathy, J. Anders, Contemp. Phys. 57, 545 (2016)
J. Anders, M. Esposito, New J. Phys. 19, 010201 (2017)
F. Campaioli, F.A. Pollock, S. Vinjanampathy, Thermodynamics in the Quantum Regime, Fundamental Aspects and New Directions (Springer, Cham, 2018)
S. Deffner, S. Campbell, Quantum Thermodynamics, An Introduction to the Thermodynamics of Quantum Information (IOP Publishing, Bristol, 2019)
R. Kosloff, J. Chem. Phys. 150, 204105 (2019)
A. Tuncer, O.E. Mustecaplioglu, (2020). arXiv:2009.04387
H.E.D. Scovil, E.O. Schulz-DuBois, Phys. Rev. Lett. 2, 262 (1959)
S. Carnot, Réflexions Sur La Puissance Motrice Du Feu et Sur Les Machines Propres à Développer Cette Puissance (Bachelier, Paris, 1824)
G. Lindblad, Commun. Math. Phys. 48, 119 (1976)
V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976)
E. Geva, R. Kosloff, J. Chem. Phys. 104(19), 7681 (1996)
C.M. Bender, D.C. Brody, B.K. Meister, J. Phys. A Math. Gen. 33, 4427 (2000)
M.O. Scully, Phys. Rev. Lett. 87, 220601 (2001)
J. He, J. Chen, B. Hua, Phys. Rev. E 65, 036145 (2002)
E. Geva, J. Mod. Opt. 49, 635 (2002)
B. Lin, J. Chen, Phys. Rev. E 67, 046105 (2003)
D. Segal, A. Nitzan, Phys. Rev. E 73, 026109 (2006)
H.T. Quan, Y.D. Wang, Y.X. Liu, C.P. Sun, F. Nori, Phys. Rev. Lett. 97, 180402 (2006)
D. Segal, Phys. Rev. Lett. 101, 260601 (2008)
Y.X. Chen, S.W. Li, Europhys. Lett. 97(4), 40003 (2012)
A. Levy, R. Kosloff, Phys. Rev. Lett. 108, 070604 (2012)
A.M. Zagoskin, S. Savel’ev, F. Nori, F.V. Kusmarsev, Phys. Rev. B 86, 014501 (2012)
O. Fialko, D.W. Hallwood, Phys. Rev. Lett. 108, 085303 (2012)
A.E. Allahverdyan, K.V. Hovhannisyan, A.V. Melkikh, S.G. Gevorkian, Phys. Rev. Lett. 111, 050601 (2013)
G.S. Agarwal, S. Chaturvedi, Phys. Rev. E 88, 012130 (2013)
L.A. Correa, J.P. Palao, G. Adesso, D. Alonso, Phys. Rev. E 87, 042131 (2013)
H.P. Goswami, U. Harbola, Phys. Rev. A 88, 013842 (2013)
D. Venturelli, R. Fazio, V. Giovannetti, Phys. Rev. Lett. 110, 256801 (2013)
D. Gelbwaser-Klimovsky, R. Alicki, G. Kurizki, Phys. Rev. E 87, 012140 (2013)
R. Alicki, Open. Syst. Inf. Dyn. 21(01n02), 1440002 (2014)
N. Brunner, M. Huber, N. Linden, S. Popescu, R. Silva, P. Skrzypczyk, Phys. Rev. E 89, 032115 (2014)
L.A. Correa, J.P. Palao, D. Alonso, G. Adesso, Sci. Rep. 4, 3949 (2014)
R. Gallego, A. Riera, J. Eisert, New J. Phys. 16(12), 125009 (2014)
R. Alicki, D. Gelbwaser-Klimovsky, K. Szczygielski, J. Phys. A Math. Theor. 49, 015002 (2016)
P.A. Erdman, F. Mazza, R. Bosisio, G. Benenti, R. Fazio, F. Taddei, Phys. Rev. B 95, 245432 (2017)
P. Chattopadhyay, G. Paul, Sci. Rep. 9, 16967 (2019)
P. Chattopadhyay, Eur. Phys. J. Plus 135, 302 (2020)
K. Ono, S..N. Shevchenko, T. Mori, S. Moriyama, F. Nori, Phys. Rev. Lett. 125, 166802 (2020)
A. Usui, W. Niedenzu, M. Huber, Phys. Rev. A 104, 042224 (2021)
G. Manzano, R. Sánchez, R. Silva, G. Haack, J.B. Brask, N. Brunner, P.P. Potts, Phys. Rev. Res. 2, 043302 (2020)
R. Dann, R. Kosloff, P. Salamon, Entropy 22, 1255 (2020)
Y. Huangfu, S. Qi, J. Jing, Phys. Lett. A 393, 127172 (2021)
T.R. de Oliveira, D. Jonathan, (2020). arXiv:2008.11694
K. Kaur, V. Singh, J. Ghai, S. Jena, O.E. Mustecaplioglu, Physica A 576, 125892 (2021)
Y. Fang, Y. Zheng, J. Chang, (2020). arXiv:2010.04856
Q. Bouton, J. Nettersheim, S. Burgardt, D. Adam, E. Lutz, A. Widera, Nat. Comm. 12, 2063 (2021)
Y. Zheng, D. Poletti, Phys. Rev. E 92, 012110 (2015)
Jefferson Luan Diniz, de Oliveira, Moisés Rojas, Cleverson Filgueiras. Phys. Rev. E 104, 014149 (2021)
S. Khandelwal, N. Brunner, G. Haack (2021). arXiv:2101.11553
S. Chatterjee, A. Koner, S. Chatterjee, C. Kumar, Phys. Rev. E 103, 062109 (2021)
P.E. Harunari, F.S. Filho, C.E. Fiore, A. Rosas, Phys. Rev. Research 3, 023194 (2021)
A. Ghoshal, S. Das, A.K. Pal, A. Sen(De), U. Sen, Phys. Rev. A 104, 042208 (2021)
V. Blickle, C. Bechinger, Nat. Phys. 7(12), 1–4 (2011)
O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt-Kaler, K. Singer, E. Lutz, Phys. Rev. Lett. 109, 203006 (2012)
J. Roßnagel, S.T. Dawkins, K.N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, K. Singer, Science 352, 325 (2016)
D. von Lindenfels, O. Gräb, C.T. Schmiegelow, V. Kaushal, J. Schulz, M.T. Mitchison, J. Goold, F. Schmidt-Kaler, U.G. Poschinger, Phys. Rev. Lett. 123, 080602 (2019)
J.P.S. Peterson, T.B. Batalhão, M. Herrera, A.M. Souza, R.S. Sarthour, I.S. Oliveira, R.M. Serra, Phys. Rev. Lett. 123, 240601 (2019)
J. Klatzow, J.N. Becker, P.M. Ledingham, C. Weinzetl, K.T. Kaczmarek, D.J. Saunders, J. Nunn, I.A. Walmsley, R. Uzdin, E. Poem, Phys. Rev. Lett. 122, 110601 (2019)
M.H.M. Passos, Alan C. Santos, Marcelo S. Sarandy, J.A.O. Huguenin, Phys. Rev. A 100, 022113 (2019)
V. Giovannetti, S. Lloyd, L. Maccone, Nat. Photonics 5, 222 (2011)
C.L. Degen, F. Reinhard, P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017)
G. Kurizki, G.A. Alvarez, A. Zwick, Technologies 5, 1 (2017)
L. Pezzè, A. Smerzi, M.K. Oberthaler, R. Schmied, P. Treutlein, Rev. Mod. Phys. 90, 035005 (2018)
P.P. Hofer, J.B. Brask, M. Perarnau-Llobet, N. Brunner, Phys. Rev. Lett. 119, 090603 (2017)
V. Mukherjee, A. Zwick, A. Ghosh, X. Chen, G. Kurizki, Commun. Phys. 2, 162 (2019)
S. Mondal, S. Bhattacharjee, A. Dutta, Phys. Rev. E 102, 022140 (2020)
S. Bhattacharjee, U. Bhattacharya, W. Niedenzu, V. Mukherjee, A. Dutta, New J. Phys. 22, 013024 (2020)
R. Alicki, M. Fannes, Phys. Rev. E 87, 042123 (2013)
K.V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, A. Acin, Phys. Rev. Lett. 111, 240401 (2013)
F. Campaioli, F.A. Pollock, F.C. Binder, L. Céleri, J. Goold, S. Vinjanampathy, K. Modi, Phys. Rev. Lett. 118, 150601 (2017)
M.G.A. Paris, Int. J. Quantum Inf. 07, 125 (2009)
J. Ma, X. Wang, C.P. Sun, F. Nori, Phys. Rep. 509, 89 (2011)
L.A. Correa, M. Mehboudi, G. Adesso, A. Sanpera, Phys. Rev. Lett. 114, 220405 (2015)
S. Zhou, M. Zhang, J. Preskill, L. Jiang, Nat. Commun. 9, 78 (2018)
A. De Pasquale, D. Rossini, R. Fazio, V. Giovannetti, Nat. Commun. 7, 12782 (2016)
G. De Palma, A. De Pasquale, V. Giovannetti, Phys. Rev. A 95, 052115 (2017)
K.V. Hovhannisyan, L.A. Correa, Phys. Rev. B 98, 045101 (2018)
S.N. Shevchenko, D.S. Karpov, Phys. Rev. Appl. 10, 014013 (2018)
M. Mehboudi, A. Sanpera, L.A. Correa, J. Phys. A Math. Theor. 52, 303001 (2019)
P.P. Potts, J.B. Brask, N. Brunner, Quantum 3, 161 (2019)
W. Muessel, H. Strobel, D. Linnemann, D.B. Hume, M.K. Oberthaler, Phys. Rev. Lett. 113, 103004 (2014)
J.B. Brask, R. Chaves, J. Kolodynski, Phys. Rev. X 5, 031010 (2015)
F. Albarelli, M.A.C. Rossi, M.G.A. Paris, M.G. Genoni, New J. Phys. 19, 123011 (2017)
E. Polino, M. Valeri, N. Spagnolo, F. Sciarrino, AVS Quantum Sci. 2, 024703 (2020)
C.M. Bender, D.C. Brody, B.K. Meister, Proc. R. Soc. Lond. A 458, 1519–1526 (2002)
J.E. Geusic, E.O. Schulz-DuBois, H.E.D. Scovil, Phys. Rev. 156, 343 (1966)
R. Alicki, J. Phys. A 12, L103 (1979)
R. Kosloff, J. Chem. Phys. 80, 1625 (1984)
E. Geva, R. Kosloff, J. Chem. Phys. 96, 3054 (1992)
E. Geva, R. Kosloff, Phys. Rev. E 49, 3903 (1994)
T. Feldmann, E. Geva, R. Kosloff, P. Salamon, Am. J. Phys. 64(4), 485–492 (1996)
R. Kosloff, E. Geva, J.M. Gordon, J. Appl. Phys. 87, 8093 (2000)
T. Feldmann, R. Kosloff, Phys. Rev. E 61, 4774 (2000)
J.P. Palao, R. Kosloff, J.M. Gordon, Phys. Rev. E 64, 056130 (2001)
T. Feldmann, R. Kosloff, Phys. Rev. E 70, 046110 (2004)
H.T. Quan, Phys. Rev. E 79, 041129 (2009)
H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)
S. Kryszewski, J. Czechowska-Kryszk, (2008). arXiv:0801.1757
R. Alicki, D. Gelbwaser-Klimovsky, G. Kurizki, arXiv:1205.4552
A. Levy, R. Alicki, R. Kosloff, Phys. Rev. E 85, 061126 (2012)
M. Kolar, D. Gelbwaser-Klimovsky, R. Alicki, G. Kurizki, Phys. Rev. Lett. 109, 090601 (2012)
R. Kosloff, A. Levy, Annu. Rev. Phys. Chem. 65, 365 (2014)
D. Gelbwaser-Klimovsky, W. Niedenzu, G. Kurizki, Adv. At. Mol. Opt. Phys. 64, 329 (2015)
V. Mukherjee, W. Niedenzu, A.G. Kofman, G. Kurizki, Phys. Rev. E 94, 062109 (2016)
G. Floquet, Sci. Ecole Norm. Sup. 12, 47–88 (1883)
M. Bukov, L. D’Alessio, A. Polkovnikov, Adv. Phys. 64(2), 139–226 (2015)
A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017)
K. Brandner, U. Seifert, Phys. Rev. E 93, 062134 (2016)
P.P. Hofer, M. Perarnau-Llobet, L.D.M. Miranda, G. Haack, R. Silva, J.B. Brask, N. Brunner, New J. Phys. 19, 123037 (2017)
H. Spohn, J. Math. Phys. 19, 1227 (1978)
K. Ono, S.N. Shevchenko, T. Mori, S. Moriyama, F. Nori, Phys. Rev. Lett. 122, 207703 (2019)
D. Gelbwaser-Klimovsky, W. Niedenzu, P. Brumer, G. Kurizki, Sci. Rep. 5, 14413 (2015)
W. Niedenzu, D. Gelbwaser-Klimovsky, G. Kurizki, Phys. Rev. E 92, 042123 (2015)
W. Niedenzu, G. Kurizki, New J. Phys. 20, 113038 (2018)
D. Gelbwaser-Klimovsky, K. Szczygielski, U. Vogl, A. Saß, R. Alicki, G. Kurizki, M. Weitz, Phys. Rev. A 91, 023431 (2015)
K. Szczygielski, D. Gelbwaser-Klimovsky, R. Alicki, Phys. Rev. E 87, 012120 (2013)
V. Mukherjee, A.G. Kofman, G. Kurizki, Commun. Phys. 3, 8 (2020)
R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)
P.C. Martin, J. Schwinger, Phys. Rev. 115, 1342 (1959)
R. Haag, N.M. Hugenholtz, M. Winnink, Commun. Math. Phys. 5, 215 (1967)
F. Tonner, G. Mahler, Phys. Rev. E 72, 066118 (2005)
D. Gelbwaser-Klimovsky, G. Kurizki, Phys. Rev. E 90, 022102 (2014)
J.B. Brask, G. Haack, N. Brunner, M. Huber, New J. Phys. 17, 113029 (2015)
D. Gelbwaser-Klimovsky, G. Kurizki, Sci. Rep. 5, 7809 (2015)
W. Niedenzu, M. Huber, E. Boukobza, Quantum 3, 195 (2019)
P. Strasberg, C.W. Wachtler, G. Schaller, Phys. Rev. Lett. 126, 180605 (2021)
K. Hammam, Y. Hassouni, R. Fazio, G. Manzano, New J. Phys. 23, 043024 (2021)
T.D. Kieu, Phys. Rev. Lett. 93, 140403 (2004)
Y. Rezek, R. Kosloff, New J. Phys. 8(5), 83 (2006)
H.T. Quan, Y.X. Liu, C.P. Sun, F. Nori, Phys. Rev. E 76, 031105 (2007)
M.J. Henrich, F. Rempp, G. Mahler, Eur. Phys. J. 151(1), 157 (2007)
H. Wang, S. Liu, J. He, Phys. Rev. E 79, 041113 (2009)
L. He, X. He, W. Tang, Sci. China Ser. G Phys. Mech. Astron. 52, 1317 (2009)
G. Thomas, R. Johal, Phys. Rev. E 83, 031135 (2011)
X. He, J. He, Sci. China Phys. Mech. Astron. 55, 1751 (2012)
X.L. Huang, T. Wang, X.X. Yi, Phys. Rev. E 86, 051105 (2012)
J. Deng, Q.H. Wang, Z. Liu, P. Hanggi, J. Gong, Phys. Rev. E 88, 062122 (2013)
K. Zhang, F. Bariani, P. Meystre, Phys. Rev. Lett. 112, 150602 (2014)
J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, E. Lutz, Phys. Rev. Lett. 112, 030602 (2014)
A. del Campo, J. Goold, M. Paternostro, Sci. Rep. 4, 6208 (2015)
M. Campisi, R. Fazio, Nat. Commun. 7, 11895 (2016)
G. Manzano, F. Galve, R. Zambrini, J.M.R. Parrondo, Phys. Rev. E 93, 052120 (2016)
R. Kosloff, Y. Rezek, Entropy 19, 136 (2017)
G. Thomas, N. Siddharth, S. Banerjee, S. Ghosh, Phys. Rev. E 97, 062108 (2018)
M. Pezzutto, M. Paternostro, Y. Omar, Quantum. Sci. Technol. 4, 025002 (2019)
N.Y. Halpern, C.D. White, S. Gopalakrishnan, G. Refael, Phys. Rev. B 99, 024203 (2019)
A. Hartmann, V. Mukherjee, W. Niedenzu, W. Lechner, Phys. Rev. Res. 2, 023145 (2020)
C. Van den Broeck, Phys. Rev. Lett. 95, 190602 (2005)
M. Esposito, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009)
M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)
M. Esposito, N. Kumar, K. Lindenberg, Phys. Rev. E 85, 031117 (2012)
C. Van den Broeck, N. Kumar, K. Lindenberg, Phys. Rev. Lett. 108, 210602 (2012)
R. Wang, J. Wang, J. He, Y. Ma, Phys. Rev. E 87, 042119 (2013)
P.A. Erdman, V. Cavina, R. Fazio, F. Taddei, V. Giovannetti, New J. Phys. 21, 103049 (2019)
F.L. Curzon, B. Ahlborn, Am. J. Phys. 43(1), 22–24 (1975)
R. Dann, A. Tobalina, R. Kosloff, Phys. Rev. Lett. 122, 250402 (2019)
R. Dann, A. Tobalina, R. Kosloff, Phys. Rev. A 101, 052102 (2020)
R. Dann, R. Kosloff, New J. Phys. 22, 013055 (2020)
F. Plastina, A. Alecce, T.J.G. Apollaro, G. Falcone, G. Francica, N. Lo Gullo, R. Zambrini, Phys. Rev. Lett. 113, 260601 (2014)
G. Francica, J. Goold, F. Plastina, Phys. Rev. E 99, 042105 (2019)
X. Chen, A. Ruschhaupt, S. Schmidt, A. Del Campo, D. Guéry-Odelin, J.G. Muga, Phys. Rev. Lett. 104, 063002 (2010)
X. Chen, J.G. Muga, Phys. Rev. A 82, 053403 (2010)
S. Masuda, K. Nakamura, Proc. R. Soc. A 466, 1135 (2010)
E. Torrontegui, S. Ibánez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, J.G. Muga, Adv. At. Mol. Opt. Phys. 62, 117 (2013)
Y.Y. Cui, X. Chen, J.G. Muga, J. Phys. Chem. A 120, 2962 (2016)
K. Funo, N. Lambert, F. Nori, C. Flindt, Phys. Rev. Lett. 124, 150603 (2020)
L. Dupays, I.L. Egusquiza, A. del Campo, A. Chenu, Phys. Rev. Res. 2, 033178 (2020)
O. Abah, E. Lutz, Phys. Rev. E 98, 032121 (2018)
O. Abah, M. Paternostro, Phys. Rev. E 99, 022110 (2019)
B. Çakmak, Ö.E. Müstecaplğlu, Phys. Rev. E 99, 032108 (2019)
K. Funo, N. Lambert, B. Karimi, J.P. Pekola, Y. Masuyama, F. Nori, Phys. Rev. B 100, 035407 (2019)
O. Abah, M. Paternostro, E. Lutz, Phys. Rev. Res. 2, 023120 (2020)
P.A. Camati, J.F.G. Santos, R.M. Serra, Phys. Rev. A 99, 062103 (2019)
M.O. Scully, M.S. Zubairy, G.S. Agarwal, H. Walther, Science 299, 862 (2003)
M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge Press, London, 1997)
A. Hardal, O. Müstecaplğlu, Sci. Rep. 5, 12953 (2015)
O. Abah, E. Lutz, Europhys. Lett. 106, 20001 (2014)
J. Rossnagel, O. Abah, F. Schmidt-Kaler, K. Singer, E. Lutz, Phys. Rev. Lett. 112, 030602 (2014)
W. Niedenzu, D. Gelbwaser-Klimovsky, A.G. Kofman, G. Kurizki, New J. Phys. 18, 083012 (2016)
J. Klaers, S. Faelt, A. Imamoglu, E. Togan, Phys. Rev. X 7, 031044 (2017)
A. de Oliveira Junior, M.C de Oliveira (2020). arXiv:2012.02049
W. Niedenzu, V. Mukherjee, A. Ghosh, A.G. Kofman, G. Kurizki, Nat. Commun. 9, 165 (2018)
J.M. Diaz de la Cruz, M.A. Martin-Delgado, Phys. Rev. A 89, 032327 (2014)
M. Beau, J. Jaramillo, A. Del Campo, Entropy 18, 168 (2016)
J. Jaramillo, M. Beau, A. Del Campo, New J. Phys. 18, 075019 (2016)
Yu-Han. Ma, Su. Shan-He, Chang-Pu. Sun, Phys. Rev. E 96, 022143 (2017)
J. Lekscha, H. Wilming, J. Eisert, R. Gallego, Phys. Rev. E 97, 022142 (2018)
Y. Chen, G. Watanabe, Y. Yu, X. Guan, A. del Campo, npj Quantum Inf. 5, 88 (2019)
D. Gelbwaser-Klimovsky, W. Kopylov, G. Schaller, Phys. Rev. A 99, 022129 (2019)
A. Hartmann, V. Mukherjee, G.B. Mbeng, W. Niedenzu, W. Lechner, Quantum 4, 377 (2020)
W. Pusz, S.L. Woronowicz, Commun. Math. Phys. 58, 273–290 (1978)
A. Lenard, J. Stat. Phys. 19, 575 (1978)
A.E. Allahverdyan, R. Balian, T.M. Nieuwenhuizen, Europhys. Lett. 67, 565 (2004)
N. Erez, G. Gordon, M. Nest, G. Kurizki, Nature 452(7188), 724–727 (2008)
D. Gelbwaser-Klimovsky, N. Erez, R. Alicki, G. Kurizki, Phys. Rev. A 88, 022112 (2013)
A. Pozas-Kerstjens, E.G. Brown, K.V. Hovhannisyan, New J. Phys. 20, 043034 (2018)
P. Abiuso, V. Giovannetti, Phys. Rev. A 99, 052106 (2019)
A. Das, V. Mukherjee, Phys. Rev. Res. 2, 033083 (2020)
D. Newman, F. Mintert, A. Nazir, Phys. Rev. E 95, 032139 (2017)
J. Iles-Smith, N. Lambert, A. Nazir, Phys. Rev. A 90, 032114 (2014)
J. Iles-Smith, A.G. Dijkstra, N. Lambert, A. Nazir, J. Chem. Phys. 144, 044110 (2016)
A.E. Allahverdyan, R.S. Johal, G. Mahler, Phys. Rev. E 77, 041118 (2008)
A.E. Allahverdyan, K. Hovhannisyan, G. Mahler, Phys. Rev. E 81, 051129 (2010)
M. Campisi, J. Pekola, R. Fazio, New J. Phys. 17, 035012 (2015)
R. Uzdin, A. Levy, R. Kosloff, Phys. Rev. X 5, 031044 (2015)
M. Campisi, R. Fazio, J. Phys. A Math. Theor. 49, 345002 (2016)
L. Buffoni, A. Solfanelli, P. Verrucchi, A. Cuccoli, M. Campisi, Phys. Rev. Lett. 122, 070603 (2019)
N. Piccione, G. De Chiara, B. Bellomo, Phys. Rev. A 103, 032211 (2021)
G. Watanabe, B.P. Venkatesh, P. Talkner, A. del Campo, Phys. Rev. Lett. 118, 050601 (2017)
G. Watanabe, B.P. Venkatesh, P. Talkner, M.-J. Hwang, A. del Campo, Phys. Rev. Lett. 124, 210603 (2020)
Z. Holmes, J. Anders, F. Mintert, Phys. Rev. Lett. 124, 210601 (2020)
R. Uzdin, A. Levy, R. Kosloff, Entropy 18, 124 (2016)
J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypczyk, J. Phys. A Math. Theor. 49, 143001 (2016)
J.C. Maxwell, Theory of Heat (Longmans, London, 1871)
K. Maruyama, F. Nori, V. Vedral, Rev. Mod. Phys. 81, 1 (2009)
L. Szilard, Z. Phys. 53, 840 (1929)
R. Landauer, IBM, J. Res. Dev. 5, 183 (1961)
R. Landauer, Phys. Lett. A 217, 188 (1996)
O. Penrose, Foundations of Statistical Mechanics: A Deductive Treatment (Pergamon, Oxford, 1970)
C.H. Bennett, Int. J. Theor. Phys. 21, 905 (1982)
C.H. Bennett, Stud. Hist. Philos. Mod. Phys. 34, 501 (2003)
W.H. Zurek, in Maxwell’s demon, Szilard’s engine and quantum measurements Frontiers of Nonequilibrium Statistical Physics, ed. by G.T. Moore, M.O. Scully (Springer, Boston, 1986), pp. 151–161
L.C. Biedenharn, J.C. Solem, Found. Phys. 25, 1221 (1995)
S. Lloyd, Phys. Rev. A 56, 3374 (1997)
J.M.R. Parrondo, Chaos 11, 725 (2001)
S.W. Kim, T. Sagawa, S. De Liberato, M. Ueda, Phys. Rev. Lett. 106, 070401 (2011)
H. Li, J. Zou, J.G. Li, B. Shao, L.A. Wu, Ann. Phys. 327, 2955 (2012)
C.Y. Cai, H. Dong, C.P. Sun, Phys. Rev. E 85, 031114 (2012)
J.J. Park, K.-H. Kim, T. Sagawa, S.W. Kim, Phys. Rev. Lett. 111, 230402 (2013)
M. Plesch, O. Dahlsten, J. Goold, V. Vedral, Sci. Rep. 4, 6995 (2014)
W.H. Zurek, Phys. Rep. 755, 21 (2018)
J. Bengtsson, M.N. Tengstrand, A. Wacker, P. Samuelsson, M. Ueda, H. Linke, S.M. Reimann, Phys. Rev. Lett. 120, 100601 (2018)
A. Aydin, A. Sisman, R. Kosloff, Entropy 22, 294 (2020)
C. Elouard, D.A. Herrera-Martí, M. Clusel, A. Auffèveset, npj Quantum Inf. 3, 9 (2017)
C. Elouard, D. Herrera-Martí, B. Huard, A. Auffèves, Phys. Rev. Lett. 118, 260603 (2017)
M.H. Mohammady, Janet Anders. New J. Phys. 19, 113026 (2017)
S.L. Braunstein, C.M. Caves, Phys. Rev. Lett. 72, 3439 (1994)
V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. Lett. 96, 010401 (2006)
Y.M. Zhang, X.W. Li, W. Yang, G.R. Jin, Phys. Rev. A 88, 043832 (2013)
T. Gefen, F. Jelezko, A. Retzker, Phys. Rev. A 96, 032310 (2017)
A. Dutta, G. Aeppli, B.K. Chakrabarti, U. Divakaran, T.F. Rosenbaum, D. Sen, Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information (Cambridge University Press, Cambridge, 2015)
P.P. Hofer, J.R. Souquet, A.A. Clerk, Phys. Rev. B 93, 041418(R) (2016)
S. Julia-Farre, T. Salamon, A. Riera, M.N. Bera, M. Lewenstein, Phys. Rev. Res. 2, 023113 (2020)
F.C. Binder, S. Vinjanampathy, K. Modi, J. Goold, New J. Phys. 17, 075015 (2015)
T.P. Le, J. Levinsen, K. Modi, M.M. Parish, F.A. Pollock, Phys. Rev. A 97, 022106 (2018)
N. Friis, M. Huber, Quantum 2, 61 (2017)
G.M. Andolina, M. Keck, A. Mari, M. Campisi, V. Giovannetti, M. Polini, Phys. Rev. Lett. 122, 047702 (2019)
D. Rossini, G.M. Andolina, M. Polini, Phys. Rev. B 100, 115142 (2019)
D. Ferraro, M. Campisi, G.M. Andolina, V. Pellegrini, M. Polini, Phys. Rev. Lett. 120, 117702 (2018)
G.M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, M. Polini, Phys. Rev. B 98, 205423 (2018)
D. Farina, G.M. Andolina, A. Mari, M. Polini, V. Giovannetti, Phys. Rev. B 99, 035421 (2019)
Y.Y. Zhang, T.R. Yang, L. Fu, X. Wang, Phys. Rev. E 99, 052106 (2019)
G.M. Andolina, M. Keck, A. Mari, V. Giovannetti, M. Polini, Phys. Rev. B 99, 205437 (2019)
A. Crescente, M. Carrega, M. Sassetti, D. Ferraro, Phys. Rev. B 102, 245407 (2020)
S. Ghosh, T. Chanda, A. Sen(De), Phys. Rev. A 101, 032115 (2020)
D. Rossini, G.M. Andolina, D. Rosa, M. Carrega, M. Polini, Phys. Rev. Lett. 125, 236402 (2020)
D. Rosa, D. Rossini, G.M. Andolina, M. Polini, M. Carrega, J. High Energy Phys. 2020, 67 (2020)
M. Carrega, J. Kim, D. Rosa, Entropy 23(5), 587 (2021)
F. Caravelli, G. Coulter-De Wit, L.P. García-Pintos, A. Hamma, Phys. Rev. Res. 2, 023095 (2020)
F. Barra, Phys. Rev. Lett. 122, 210601 (2019)
K.V. Hovhannisyan, A. Imparato, New J. Phys. 21, 052001 (2019)
J. Liu, D. Segal, G. Hanna, J. Phys. Chem. C 123(30), 18303 (2019)
K.V. Hovhannisyan, F. Barra, A. Imparato, Phys. Rev. Res. 2, 033413 (2020)
J.Q. Quach, W.J. Munro, Phys. Rev. Appl. 14, 024092 (2020)
M. Carrega, A. Crescente, D. Ferraro, M. Sassetti, New J. Phys. 22, 083085 (2020)
S. Zakavati, F.T. Tabesh, S. Salimi, (2020). arXiv:2003.09814
S. Ghosh, T. Chanda, S. Mal, A. Sen De, Phys. Rev. A 104, 032207 (2021)
S. Bai, J. An, Phys. Rev. A 102, 060201(R) (2020)
A. Crescente, M. Carrega, M. Sassetti, D. Ferraro, New J. Phys. 22, 063057 (2020)
T. Purves, T. Short, Phys. Rev. E 104, 014111 (2021)
Mark T. Mitchison, John Goold, Javier Prior, Quantum 5, 500 (2021)
J.Q. Quach, K.E. McGhee, L. Ganzer, D.M. Rouse, B.W. Lovett, E.M. Gauger, J. Keeling, G. Cerullo, D.G. Lidzey, T. Virgili, (2020). arXiv:2012.06026
A.E. Allahverdyan, Th.M. Nieuwenhuizen, Phys. A 305, 542 (2002)
G. Francica, J. Goold, F. Plastina, M. Paternostro, npj Quantum Inf. 3, 12 (2017)
J. Monsel, M. Fellous-Asiani, B. Huard, A. Auff’eves, Phys. Rev. Lett. 124, 130601 (2020)
G. Francica, F.C. Binder, G. Guarnieri, M.T. Mitchison, J. Goold, F. Plastina, Phys. Rev. Lett. 125, 180603 (2020)
S. Deffner, E. Lutz, J. Phys. A Math. Theor. 46, 335302 (2013)
S. Deffner, S. Campbell, J. Phys. A Math. Theor. 50, 453001 (2017)
I. Bengtsson, K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. (Cambridge University Press, Cambridge, 2017)
M.L. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
L. Mandelstam, I. Tamm, J. Phys. 9, 249 (1945)
L.B. Levitin, Y. Toffoli, Phys. Rev. Lett. 103, 160502 (2009)
N. Margolus, L.B. Levitin, Phys. D 120, 188 (1998)
L. Gurvits, H. Barnum, Phys. Rev. A 66, 062311 (2002)
L. Gurvits, H. Barnum, Phys. Rev. A 72, 032322 (2005)
Z. Chen, Phys. Rev. A 71, 052302 (2005)
O. Guhne, G. Toth, H.J. Briegel, New J. Phys. 7, 229 (2005)
G. Toth, Phys. Rev. A 85, 022322 (2012)
P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, A. Smerzi, Phys. Rev. A 85, 022321 (2012)
J. Kim, D. Rosa, D. Safranek, (2021). arXiv:2108.02491
H.J. Lipkin, N. Meshkov, A.J. Glick, Nucl. Phys. A 62, 188 (1965)
R.H. Dicke, Phys. Rev. 93, 99 (1954)
P.W. Anderson, Phys. Rev. 109, 1492 (1958)
R. Nandkishore, D.A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015)
F. Alet, N. Laflorencie, C. R. Phys. 19, 498 (2018)
D.A. Abanin, E. Altman, I. Bloch, M. Serbyn, Rev. Mod. Phys. 91, 021001 (2019)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)
P. Calabrese, J. Cardy, Entanglement entropy and quantum field theory. J. Stat. Mech. Theory Exp. P06002 (2004)
A.C. Santos, B. Cakmak, S. Campbell, N.T. Zinner, Phys. Rev. E 100, 032107 (2019)
A.C. Santos, A. Saguia, M.S. Sarandy, Phys. Rev. E 101, 062114 (2020)
F.H. Kamin, F.T. Tabesh, S. Salimi, F. Kheirandish, A.C. Santos, New J. Phys. 22(8), 083007 (2020)
S. Gherardini, F. Campaioli, F. Caruso, F.C. Binder, Phys. Rev. Res. 2, 013095 (2020)
F. Caravelli, B. Yan, L.P. Garcia-Pintos, A. Hamma, Quantum 5, 505 (2021)
A. Tavakoli, G. Haack, N. Brunner, J.B. Brask, Phys. Rev. A 101, 012315 (2020)
S. Khandelwal, N. Palazzo, N. Brunner, G. Haack, New J. Phys. 22, 073039 (2020)
M. Josefsson, M. Leijnse, Phys. Rev. B 101, 081408(R) (2020)
L. Bresque, P..A. Camati, S. Rogers, K. Murch, A..N. Jordan, A. Auffèves, Phys. Rev. Lett. 126, 120605 (2020)
J. Yi, P. Talkner, Y.W. Kim, Phys. Rev. E 96, 022108 (2017)
X. Ding, J. Yi, Y.W. Kim, P. Talkner, Phys. Rev. E 98, 042122 (2018)
Acknowledgements
We are grateful to Utso Bhattacharya, Victor Mukherjee, Wolfgang Niedenzu, and Saikat Mondal for collaboration and useful discussions on related works. We also thank Arnab Ghosh, Souvik Bandyopadhyay, and Somnath Maity for critical comments and suggestions. S.B. acknowledges CSIR, India for financial support. A.D. acknowledges financial support from SPARC program, MHRD, India and SERB, DST, India.
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Bhattacharjee, S., Dutta, A. Quantum thermal machines and batteries. Eur. Phys. J. B 94, 239 (2021). https://doi.org/10.1140/epjb/s10051-021-00235-3
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DOI: https://doi.org/10.1140/epjb/s10051-021-00235-3