Abstract
In the preceding Chap. 7, we derived a general fluctuation theorem (FT) in detailed and integral form valid for a broad class of CPTP quantum maps, which model a variety of quantum evolutions as we explained in more detail in Chap. 2. In this chapter we clarify and extend these previous results by considering together the system and its surroundings. By tracing over the environment degrees of freedom, we can then recover the quantum map description for the reduced open system dynamics.
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Notes
- 1.
We also exclude here the possibility of further implementation of feedback protocols using local measurements and classical communication of the results.
- 2.
Note however that the converse statement is not necessarily true, i.e. we may have for different values of \(\mu \) and \(\nu \) the same value of \(\Delta \phi _{\mu \nu }\)
References
M. Campisi, P. Talkner, P. Hänggi, Fluctuation theorems for continuously monitored quantum fluxes. Phys. Rev. Lett. 105, 140601 (2010)
M. Esposito, U. Harbola, S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems. Rev. Mod. Phys. 81, 1665–1702 (2009)
T. Hatano, S.-I. Sasa, Steady-state thermodynamics of Langevin systems. Phys. Rev. Lett. 86, 3463 (2001)
U. Seifert, Entropy production along a Stochastic trajectory and an integral fluctuation theorem. Phys. Rev. Lett. 95, 040602 (2005)
M. Esposito, C. Van den Broeck, Three detailed fluctuation theorems. Phys. Rev. Lett. 104, 090601 (2010)
U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75, 126001 (2012)
J.P. Pekola, P. Solinas, A. Shnirman, D.V. Averin, Calorimetric measurement of work in a quantum system. New J. Phys. 15, 115006 (2013)
S. Gasparinetti, K.L. Viisanen, O.-P. Saira, T. Faivre, M. Arzeo, M. Meschke, J.P. Pekola, Fast electron thermometry for ultrasensitive calorimetric detection. Phys. Rev. Appl. 3, 014007 (2015)
S. Suomela, A. Kutvonen, T. Ala-Nissila, Quantum jump model for a system with a finite-size environment. Phys. Rev. E 93, 062106 (2016)
M.O. Scully, M.S. Zubairy, G.S. Agarwal, H. Walther, Extracting work from a single heat bath via vanishing quantum coherence. Science 299, 862–864 (2003)
A.Ü.C. Hardal, Ö.E. Müstecaplıoğlu, Superradiant quantum heat engine. Sci. Rep. 5, 12953 (2015)
R. Dillenschneider, E. Lutz, Energetics of quantum correlations. Europhys. Lett. 88, 50003 (2009)
X.L. Huan, T. Wang, X.X. Yi, Effects of reservoir squeezing on quantum systems and work extraction. Phys. Rev. E 86, 051105 (2012)
J. Roßnagel, O. Abah, F. Schmidt-Kaler, K. Singer, E. Lutz, Nanoscale heat engine beyond the carnot limit. Phys. Rev. Lett. 112, 030602 (2014)
L.A. Correa, J.P. Palao, D. Alonso, G. Adesso, Quantumenhanced absorption refrigerators. Sci. Rep., 3949 (2014)
D. Reeb, M.M. Wolf, An improved Landauer principle with finite-size corrections. New J. Phys. 16, 103011 (2014)
J. Goold, M. Paternostro, K. Modi, Nonequilibrium quantum landauer principle. Phys. Rev. Lett. 114, 060602 (2015)
O. Abah, E. Lutz, Efficiency of heat engines coupled to nonequilibrium reservoirs. Europhys. Lett. 106, 20001 (2014)
G. Manzano, F. Galve, R. Zambrini, J.M.R. Parrondo, Entropy production and thermodynamic power of the squeezed thermal reservoir. Phys. Rev. E 93, 052120 (2016)
W. Niedenzu, D. Gelbwaser-Klimovsky, A.G. Kofman, G. Kurizki, On the operation of machines powered by quantum nonthermal baths. New J. Phys. 18, 083012 (2016)
M. Esposito, K. Lindenberg, C. Van den Broeck, Entropy production as correlation between system and reservoir. New J. Phys. 12, 013013 (2010)
S. Deffner, E. Lutz, Nonequilibrium entropy production for open quantum systems. Phys. Rev. Lett. 107, 140404 (2011)
T. Sagawa, Second law-like inequalitites with quantum relative entropy: an introduction, in lectures on quantum computing, thermodynamics and statistical physics, in Kinki University Series on Quantum Computing, ed. by M. Nakahara (World Scientific, USA, 2013)
J.M. Horowitz, J.M.R. Parrondo, Entropy production along nonequilibrium quantum jump trajectories. New. J. Phys 15, 085028 (2013)
B. Leggio, A. Napoli, A. Messina, H.P. Breuer, Entropy production and information fluctuations along quantum trajectories. Phys. Rev. A 88, 042111 (2013)
S. Deffner, Quantum entropy production in phase space. Europhys. Lett. 103, 30001 (2013)
K. Funo, Y. Watanabe, M. Ueda, Integral quantum fluctuation theorems under measurement and feedback control. Phys. Rev. E 88, 052121 (2013)
F. Fagnola, R. Rebolledo, Entropy production for quantum Markov semigroups. Commun. Math. Phys. 335, 547–570 (2015)
M. Esposito, M.A. Ochoa, M. Galperin, Quantum thermodynamics: a nonequilibrium Green’s function approach. Phys. Rev. Lett. 114, 080602 (2015)
G. Manzano, J.M. Horowitz, J.M.R. Parrondo, Nonequilibrium potential and fluctuation theorems for quantum maps. Phys. Rev. E 92, 032129 (2015)
M. Esposito, C. Van den Broeck, Three faces of the second law. I. Master equation formulation. Phys. Rev. E 82, 011143 (2010)
C. Van den Broeck, M. Esposito, Three faces of the second law. II. Fokker-Planck formulation. Phys. Rev. E 82, 011144 (2010)
B. Groisman, S. Popescu, A. Winter, Quantum, classical, and total amount of correlations in a quantum state. Phys. Rev. A 72, 032317 (2005)
K. Kraus, A. Böhm, J.D. Dollard, W.H. Wootters, States, Effects, and Operations : Fundamental Notions of Quantum Theory, Lecture notes in physics (Springer, Berlin, 1983)
J.M.R. Parrondo, J.M. Horowitz, T. Sagawa, Thermodynamics of information. Nat. Phys. 11, 131–139 (2015)
K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)
S. Luo, Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)
F. Haake, Quantum Signatures of Chaos, 3rd edn. Springer series in synergetics (Springer, Berlin, 2010)
J. Anders, Thermal state entanglement in harmonic lattices. Phys. Rev. A 77, 062102 (2008)
M. Campisi, P. Hänggi, P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications. Rev. Mod. Phys. 83, 771–791 (2011)
T. Monnai, Unified treatment of the quantum fluctuation theorem and the Jarzynski equality in terms of microscopic reversibility. Phys. Rev. E 72, 027102 (2005)
J.M. Horowitz, Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator. Phys. Rev. E 85, 031110 (2012)
T. Sagawa, M. Ueda, Role of mutual information in entropy production under information exchanges. New J. Phys. 15, 125012 (2013)
G.E. Crooks, Quantum operation time reversal. Phys. Rev. A 77, 034101 (2008)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
H. Spohn, Entropy production for quantum dynamical semigroups. J. Math. Phys. 19, 1227–1230 (1978)
J.M. Horowitz, T. Sagawa, Equivalent definitions of the quantum nonadiabatic entropy production. J. Stat. Phys. 156, 55–65 (2014)
H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2010)
A. Rivas, S.F. Huelga, Open Quantum Systems : An Introduction (Springer, Berlin, 2012)
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Manzano Paule, G. (2018). Entropy Production Fluctuations in Quantum Processes. In: Thermodynamics and Synchronization in Open Quantum Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-93964-3_8
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