Quantum Thermodynamics with Measurement Processes

[1] S. Carnot, Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power (Paris: Bachelier, 1824).

[2] J. C. Maxwell, Theory of heat (Appleton, London, 1871), p. 330.

[3] L. Szilard, “Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen”, Zeitschrift für Physik 53, 840 (1929).

[4] E. Fermi, Thermodynamics (Dover books on physics, 1956).

[5] R. Landauer, “Irreversibility and Heat Generation in the Computing Process”, IBM Journal of Research and Development 5, 183 (1961).

[6] H. J. Groenewold, “A Problem of Information Gain by Quantal Measurements”, International Journal of Theoretical Physics 4, 327 (1971).

[7] A. Lenard, “Thermodynamical proof of the Gibbs formula for elementary quantum systems”, Journal of Statistical Physics 19, 575 (1978).

[8] W. Pusz and S. L. Woronowicz, “Passive states and KMS states for general quantum systems”, Communications in Mathematical Physics 58, 273 (1978).

[9] R. Alicki, “The quantum open system as a model of the heat engine”, Journal of Physics A: Mathematical and General 12, L103 (1979).

[10] C. Kittel and H. Kroemer, Thermal Physics, 2nd ed (W. H. Freeman, New York, 1980).

[11] C. H. Bennett, “The thermodynamics of computation—a review”, International Journal of Theoretical Physics 21, 905 (1982).

[12] M. Ozawa, “Quantum measuring processes of continuous observables”, Journal of Mathematical Physics 25, 79 (1984).

[13] J. J. Sakurai, Modern Quantum Mechanics, edited by S. F. Tuan, Rev. ed (Addison- Wesley, Reading, Mass.; Tokyo, 1994).

[14] C. Jarzynski, “Equilibrium free-energy differences from nonequilibrium measure- ments: A master-equation approach”, Physical Review E 56, 5018 (1997).

[15] C. Jarzynski, “Nonequilibrium Equality for Free Energy Differences”, Physical Re- view Letters 78, 2690 (1997).

[16] J. Kurchan, “Fluctuation theorem for stochastic dynamics”, Journal of Physics A: Mathematical and General 31, 3719 (1998).

[17] M. B. Mensky, “Decoherence and the theory of continuous quantum measure- ments”, Physics-Uspekhi 923, 55 (1998), arXiv:9812017 [quant-ph].

[18] G. E. Crooks, “Entropy production fiuctuation theorem and the nonequilibrium work relation for free energy differences”, Physical Review E 60, 2721 (1999).

[19] T. Hatano, “Jarzynski equality for the transitions between nonequilibrium steady states.”, Physical Review E 60, R5017 (1999).

[20] C. Maes, “The fiuctuation theorem as a Gibbs property”, Journal of Statistical Physics 95, 367 (1999).

[21] Y. Ishii and T. Yanagida, “Single Molecule Detection in Life Sciences”, Single Molecules 1, 5 (2000).

[22] C. Jarzynski, “Hamiltonian derivation of a detailed fiuctuation theorem”, Journal of Statistical Physics 98, 77 (2000).

[23] J. Kurchan, “A Quantum Fluctuation Theorem”, Preprint (2000), arXiv:0007360 [cond-mat].

[24] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge university press, Cambridge, 2000).

[25] H. Tasaki, “Jarzynski Relations for Quantum Systems and Some Applications”, Preprint (2000), arXiv:0009244 [cond-mat].

[26] H. Tasaki, “Statistical mechanical derivation of the second law of thermodynam- ics”, Preprint (2000), arXiv:0009206 [cond-mat].

[27] S. Yukawa, “A Quantum Analogue of the Jarzynski Equality”, Journal of the Phys- ical Society of Japan 69, 2367 (2000).

[28] D. J. Evans and D. J. Searles, “The Fluctuation Theorem”, Advances in Physics 51, 1529 (2002).

[29] H. S. Leff and A. F. Rex, eds., Maxwell’s demon 2: Entropy, classical and quantum information, computing, 2nd ed. (Institute of Physics, London, 2003).

[30] W. De Roeck and C. Maes, “Quantum version of free-energy–irreversible-work re- lations”, Physical Review E 69, 026115 (2004).

[31] C. Jarzynski, “Classical and Quantum Fluctuation Theorems for Heat Exchange”, Physical Review Letters 92, 230602 (2004).

[32] T. Kieu, “The Second Law, Maxwell’s Demon, and Work Derivable from Quantum Heat Engines”, Physical Review Letters 93, 140403 (2004).

[33] D. Collin, F. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco, and C. Bustamante, “Veri- fication of the Crooks fiuctuation theorem and recovery of RNA folding free ener- gies”, Nature 437, 231 (2005), arXiv:0512266 [cond-mat].

[34] T. Monnai, “Unified treatment of the quantum fiuctuation theorem and the Jarzyn- ski equality in terms of microscopic reversibility”, Physical Review E 72, 027102 (2005).

[35] U. Seifert, “Entropy Production along a Stochastic Trajectory and an Integral Fluc- tuation Theorem”, Physical Review Letters 95, 040602 (2005).

[36] M. Esposito and S. Mukamel, “Fluctuation theorems for quantum master equa- tions”, Physical Review E 73, 046129 (2006).

[37] C. Jarzynski, “Comparison of far-from-equilibrium work relations”, Comptes Ren- dus Physique 8, 495 (2007), arXiv:0612305 [cond-mat].

[38] R. Kawai, J. Parrondo, and C. den Broeck, “Dissipation: The Phase-Space Perspec- tive”, Physical Review Letters 98, 080602 (2007).

[39] H. T. Quan, Y.-x. Liu, C. P. Sun, and F. Nori, “Quantum thermodynamic cycles and quantum heat engines”, Physical Review E 76, 031105 (2007), arXiv:0611275 [quant-ph].

[40] P. Talkner and P. Hänggi, “The Tasaki–Crooks quantum fiuctuation theorem”, Journal of Physics A: Mathematical and Theoretical 40, F569 (2007).

[41] P. Talkner, E. Lutz, and P. Hänggi, “Fluctuation theorems: Work is not an observ- able”, Physical Review E 75, 050102 (2007), arXiv:0612305 [cond-mat].

[42] D. Andrieux and P. Gaspard, “Quantum Work Relations and Response Theory”, Physical Review Letters 230404, 7 (2008).

[43] F. G. S. L. Brandão and M. B. Plenio, “Entanglement theory and the second law of thermodynamics”, Nature Physics 4, 873 (2008).

[44] G. E. Crooks, “On the Jarzynski relation for dissipative quantum dynamics”, Jour- nal of Statistical Mechanics: Theory and Experiment 2008, P10023 (2008).

[45] C. Jarzynskia, “Nonequilibrium work relations: foundations and applications”, The European Physical Journal B 64, 331 (2008).

[46] T. Sagawa and M. Ueda, “Second Law of Thermodynamics with Discrete Quantum Feedback Control”, Physical Review Letters 100, 080403 (2008).

[47] S. Akagawa and N. Hatano, “The Exchange Fluctuation Theorem in Quantum Me- chanics”, Progress of Theoretical Physics 121, 1157 (2009).

[48] M. Campisi, P. Talkner, and P. Hänggi, “Fluctuation Theorem for Arbitrary Open Quantum Systems”, Physical Review Letters 102, 210401 (2009).

[49] M. Esposito, “Nonequilibrium fiuctuations, fiuctuation theorems, and counting statistics in quantum systems”, Reviews of Modern Physics 81, 1665 (2009).

[50] K. Jacobs, “Second law of thermodynamics and quantum feedback control: Maxwell’s demon with weak measurements”, Physical Review A 80, 012322 (2009), arXiv:0906.4146.

[51] G. Kimura, “ELEMENTARY MATHEMATICAL FRAMEWORK FOR OPEN QUANTUM d-LEVEL SYSTEMS: DECOHERENCE OVERVIEW”, in Decoherence suppression in quantum systems 2008, edited by M. Nakahara, R. Rahimi, and A. SaiToh (2009), pp. 1–51.

[52] O. Maroney, “Generalizing Landauer’s principle”, Physical Review E 79, 031105 (2009).

[53] K. Maruyama, F. Nori, and V. Vedral, “Colloquium: The physics of Maxwell’s de- mon and information”, Reviews of Modern Physics 81, 1 (2009).

[54] T. Sagawa and M. Ueda, “Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure”, Physical Review Letters 102, 250602 (2009).

[55] M. Campisi, P. Talkner, and P. Hänggi, “Fluctuation Theorems for Continuously Monitored Quantum Fluxes”, Physical Review Letters 105, 140601 (2010).

[56] M. Esposito, K. Lindenberg, and C. Van den Broeck, “Entropy production as cor- relation between system and reservoir”, New Journal of Physics 12, 013013 (2010), arXiv:0908.1125.

[57] H.-H. Hasegawa, J. Ishikawa, K. Takara, and D. Driebe, “Generalization of the sec- ond law for a nonequilibrium initial state”, Physics Letters A 374, 1001 (2010), arXiv:0907.1569.

[58] J. M. Horowitz and S. Vaikuntanathan, “Nonequilibrium detailed fiuctuation the- orem for repeated discrete feedback”, Physical Review E 82, 061120 (2010).

[59] S. Nakamura et al., “Nonequilibrium Fluctuation Relations in a Quantum Coher- ent Conductor”, Physical Review Letters 104, 080602 (2010).

[60] M. Ponmurugan, “Generalized detailed fiuctuation theorem under nonequilib- rium feedback control”, Physical Review E 82, 031129 (2010).

[61] J. Ren, P. Hänggi, and B. Li, “Berry-phase-induced heat pumping and its impact on the fiuctuation theorem”, Physical review letters 170601, 1 (2010).

[62] T. Sagawa and M. Ueda, “Generalized Jarzynski Equality under Nonequilibrium Feedback Control”, Physical Review Letters 104, 090602 (2010).

[63] K. Takara, H.-H. Hasegawa, and D. Driebe, “Generalization of the second law for a transition between nonequilibrium states”, Physics Letters A 375, 88 (2010), arXiv:0907.1569.

[64] J. Teifel and G. Mahler, “Limitations of the quantum Jarzynski estimator: Boundary switching processes”, European Physical Journal B 75, 275 (2010).

[65] S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, “Experimental demon- stration of information-to-energy conversion and validation of the generalized Jarzynski equality”, Nature Physics 6, 988 (2010), arXiv:1009.5287.

[66] M. Campisi, P. Hänggi, and P. Talkner, “Colloquium: Quantum fiuctuation rela- tions: Foundations and applications”, Reviews of Modern Physics 83, 771 (2011).

[67] M. Campisi, P. Talkner, and P. Hänggi, “Infiuence of measurements on the statistics of work performed on a quantum system”, Physical Review E 83, 041114 (2011), arXiv:1101.2404.

[68] S. De Liberato and M. Ueda, “Carnot’s theorem for nonthermal stationary reser- voirs”, Physical Review E 84, 051122 (2011).

[69] M. Esposito and C. Van den Broeck, “Second law and Landauer principle far from equilibrium”, Europhysics Letters 95, 40004 (2011), arXiv:1104.5165.

[70] S. W. Kim, T. Sagawa, S. De Liberato, and M. Ueda, “Quantum Szilard Engine”, Physical Review Letters 106, 070401 (2011).

[71] Y. Morikuni and H. Tasaki, “Quantum Jarzynski-Sagawa-Ueda relations”, Journal of Statistical Physics 143, 1 (2011), arXiv:1012.2753.

[72] S. Nakamura et al., “Fluctuation theorem and microreversibility in a quantum co- herent conductor”, Physical Review B 83, 155431 (2011).

[73] J. M. R. Parrondo and J. M. Horowitz, “Maxwell’s demon in the quantum world”, Physics 4, 13 (2011).

[74] T. Sagawa, “Hamiltonian Derivations of the Generalized Jarzynski Equalities un- der Feedback Control”, Journal of Physics: Conference Series 297, 012015 (2011).

[75] A. Bednorz, W. Belzig, and A. Nitzan, “Nonclassical time correlation functions in continuous quantum measurement”, New Journal of Physics 14, 013009 (2012).

[76] S. Deffner and E. Lutz, “Information free energy for nonequilibrium states”, Preprint (2012), arXiv:1201.3888.

[77] D. Kafri and S. Deffner, “Holevo’s bound from a general quantum fiuctuation the- orem”, Physical Review A 86, 044302 (2012).

[78] H. T. Quan and C. Jarzynski, “Validity of nonequilibrium work relations for the rapidly expanding quantum piston”, Physical Review E 85, 031102 (2012), arXiv:arXiv:1112.5798v1.

[79] S. Rana, S. Lahiri, and A. M. Jayannavar, “Quantum Jarzynski equality with mul- tiple measurement and feedback for isolated system”, Pramana 79, 233 (2012).

[80] T. Sagawa, “Second law-like inequalities with quantum relative entropy: an in- troduction”, in Lectures on quantum computing, thermodynamics and statistical physics, edited by M. Nakahara and S. Tanaka (World Scientific, 2012) Chap. 3, pp. 125–190, arXiv:1202.0983.

[81] T. Sagawa, “Thermodynamics of information processing in small systems”, Progress of Theoretical Physics 127, 1 (2012).

[82] T. Sagawa and M. Ueda, “Information Thermodynamics: Maxwell’s Demon in Nonequilibrium Dynamics”, in Nonequilibrium statistical physics of small systems: fluctuation relations and beyond, edited by R. Klages, W. Just, and C. Jarzynski (Wiley-VCH, Weinheim, 2012), arXiv:1111.5769.

[83] U. Seifert, “Stochastic thermodynamics, fiuctuation theorems and molecular ma- chines.”, Reports on progress in physics. Physical Society (Great Britain) 75, 126001 (2012), arXiv:1205.4176.

[84] T. Albash, D. A. Lidar, M. Marvian, and P. Zanardi, “Fluctuation theorems for quan- tum processes”, Physical Review E 88, 032146 (2013), arXiv:1212.6589.

[85] J. Anders and V. Giovannetti, “Thermodynamics of discrete quantum processes”, New Journal of Physics 15, 033022 (2013), arXiv:1211.0183.

[86] M. Campisi, “Quantum fiuctuation relations for ensembles of wave functions”, New Journal of Physics 15, 115008 (2013), arXiv:1306.5557.

[87] S. Deffner, “Quantum entropy production in phase space”, Europhysics Letters 103, 30001 (2013), arXiv:1307.3183.

[88] K. Funo, Y. Watanabe, and M. Ueda, “Integral quantum fiuctuation theorems un- der measurement and feedback control”, Physical Review E 88, 052121 (2013), arXiv:1307.2362.

[89] M. Horodecki and J. Oppenheim, “Fundamental limitations for quantum and nanoscale thermodynamics”, Nature Communications 4, 1 (2013).

[90] J. V. Koski, T. Sagawa, O.-P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Möttönen, T. Ala-Nissila, and J. P. Pekola, “Distribution of entropy production in a single- electron box”, Nature Physics 9, 644 (2013).

[91] B. Leggio, A. Napoli, A. Messina, and H.-P. Breuer, “Entropy production and in- formation fiuctuations along quantum trajectories”, Physical Review A 88, 042111 (2013), arXiv:1305.6733v2.

[92] Y. Morikuni and H. Tajima, “Quantum Jarzynski equalities for the energy costs of the information processes”, Preprint (2013), arXiv:1312.6022.

[93] H. Tajima, “Mesoscopic Thermodynamics based on Quantum Information The- ory”, Ph. D. Thesis (The University of Tokyo, 2013).

[94] H. Tajima, “Minimal energy cost of thermodynamic information processes only with entanglement transfer”, Preprint (2013), arXiv:1311.1285.

[95] H. Tajima, “Second law of information thermodynamics with entanglement trans- fer”, Physical Review E 88, 042143 (2013), arXiv:1212.0407.

[96] J. Åberg, “Catalytic Coherence”, Physical Review Letters 113, 150402 (2014), arXiv:1304.1060.

[97] S. An, J.-N. Zhang, M. Um, D. Lv, Y. Lu, J. Zhang, Z.-Q. Yin, H. T. Quan, and K. Kim, “Experimental test of the quantum Jarzynski equality with a trapped-ion system”, Nature Physics 11, 193 (2014), arXiv:1409.4485.

[98] T. B. Batalhão et al., “Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed Quantum System”, Physical Review Letters 113, 140601 (2014).

[99] J. Goold and K. Modi, “Energetic fiuctuations in an open quantum process”, Preprint (2014), arXiv:1407.4618.

[100] Y. Murashita, K. Funo, and M. Ueda, “Nonequilibrium equalities in absolutely ir- reversible processes”, Physical Review E 90, 042110 (2014), arXiv:1401.4494.

[101] A. E. Rastegin and K. Życzkowski, “Jarzynski equality for quantum stochastic maps”, Physical Review E 89, 012127 (2014), arXiv:1307.5370.

[102] P. Skrzypczyk, A. J. Short, and S. Popescu, “Work extraction and thermodynam- ics for individual quantum systems”, Nature Communications 5, 4185 (2014), arXiv:1307.1558.

[103] H. Tajima, “A New Second Law of Information Thermodynamics Using Entan- glement Measure”, in Proceedings of the 12th asia pacific physics conference, Vol. 012129 (2014), pp. 1–4.

[104] G. Watanabe, B. P. Venkatesh, P. Talkner, M. Campisi, and P. Hänggi, “Quantum fiuctuation theorems and generalized measurements during the force protocol”, Physical Review E 89, 032114 (2014), arXiv:1312.7104.

[105] F. Brandão, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, “The second laws of quantum thermodynamics”, Proceedings of the National Academy of Sciences 112, 3275 (2015), arXiv:1305.5278.

[106] K. Funo, Y. Murashita, and M. Ueda, “Quantum nonequilibrium equalities with absolute irreversibility”, New Journal of Physics 17, 075005 (2015).

[107] Z. Gong and H. T. Quan, “Jarzynski equality, Crooks fiuctuation theorem, and the fiuctuation theorems of heat for arbitrary initial states”, Physical Review E - Statis- tical, Nonlinear, and Soft Matter Physics 92 (2015), arXiv:1503.05036.

[108] M. Hayashi, S. Ishizaka, A. Kawachi, G. Kimura, and T. Ogawa, Introduction to Quantum Information Science, Graduate Texts in Physics (Springer Berlin Heidel- berg, Berlin, Heidelberg, 2015).

[109] C. Jarzynski, H. T. Quan, and S. Rahav, “Quantum-Classical Correspondence Prin- ciple for Work Distributions”, Physical Review X 5, 031038 (2015), arXiv:1507 . 05763.

[110] A. S. L. Malabarba, A. J. Short, and P. Kammerlander, “Clock-driven quantum ther- mal engines”, New Journal of Physics 17, 045027 (2015).

[111] J. M. R. Parrondo, J. M. Horowitz, and T. Sagawa, “Thermodynamics of informa- tion”, Nature Physics 11, 131 (2015).

[112] B. Prasanna Venkatesh, G. Watanabe, and P. Talkner, “Quantum fiuctuation the- orems and power measurements”, New Journal of Physics 17, 075018 (2015), arXiv:1503.03228.

[113] N. Shiraishi and T. Sagawa, “Fluctuation theorem for partially masked nonequilib- rium dynamics”, Physical Review E 91, 012130 (2015), arXiv:1403.4018.

[114] H. Tasaki, “Quantum Statistical Mechanical Derivation of the Second Law of Ther- modynamics: A Hybrid Setting Approach”, Physical Review Letters 116, 170402 (2016), arXiv:1511.01999.

[115] H. Tasaki, Typicality of Thermal Equilibrium and Thermalization in Isolated Macro- scopic Quantum Systems, Vol. 163, 5 (Springer US, 2016), pp. 937–997, arXiv:1507. 06479.

[116] S. Vinjanampathy and J. Anders, “Quantum thermodynamics”, Contemporary Physics 57, 545 (2016).

[117] M. Hayashi and H. Tajima, “Measurement-based formulation of quantum heat en- gines”, Physical Review A 95, 032132 (2017), arXiv:1504.06150v4.

[118] E. Iyoda, K. Kaneko, and T. Sagawa, “Fluctuation Theorem for Many-Body Pure Quantum States”, Physical Review Letters 119, 100601 (2017), arXiv:1712.05172.

[119] Y. Morikuni, H. Tajima, and N. Hatano, “Quantum Jarzynski equality of measurement-based work extraction”, Physical Review E 95, 032147 (2017), arXiv:1610.06316.

[120] M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, and A. Acin, “No- Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems”, Physical Review Letters 118, 070601 (2017), arXiv:1606.08368.

[121] J. Åberg, “Fully Quantum Fluctuation Theorems”, Physical Review X 8, 011019 (2018), arXiv:1601.01302.

[122] H. Tajima, N. Shiraishi, and K. Saito, “Uncertainty Relations in Implementation of Unitary Operations”, Physical Review Letters 121, 110403 (2018).