Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems

Reviews of Modern Physics

Volumn 81, Issue 4, 2009, Pages 1665-1702

  Esposito, Massimiliano ^a   Harbola, Upendra ^b   Mukamel, Shaul ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; GREEN COMPUTING; OPEN SYSTEMS; QUANTUM OPTICS;

COUNTING STATISTICS; FLUCTUATION THEOREMS; NON-EQUILIBRIUM STEADY STATE; NONEQUILIBRIUM BOUNDARIES; NONEQUILIBRIUM FLUCTUATIONS; PARTICLE STATISTICS; QUANTUM MASTER EQUATIONS; UNIVERSAL PROPERTIES;

QUANTUM CHEMISTRY;

EID: 72449206663     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.81.1665     Document Type: Article

References (204)

1. Allahverdyan, A. E., and T. M. Nieuwenhuizen, 2005, " Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems, " Phys. Rev. E 71, 066102. 10.1103/PhysRevE.71.066102
2. Andrieux, D., and P. Gaspard, 2004, " Fluctuation theorem and Onsager reciprocity relations, " J. Chem. Phys. 121, 6167. 10.1063/1.1782391
3. Andrieux, D., and P. Gaspard, 2006, " Fluctuation theorem for transport in mesoscopic systems, " J. Stat. Mech.: Theory Exp. 2006, P01011. 10.1088/1742-5468/2006/01/P01011
4. Andrieux, D., and P. Gaspard, 2007a, " A fluctuation theorem for currents and non-linear response coefficients, " J. Stat. Mech.: Theory Exp. 2007, P02006. 10.1088/1742-5468/2007/02/P02006
5. Andrieux, D., and P. Gaspard, 2007b, " Fluctuation theorem for currents and Schnakenberg network theory, " J. Stat. Phys. 127, 107. 10.1007/s10955-006-9233-5
6. Andrieux, D., and P. Gaspard, 2008, " Quantum work relations and response theory, " Phys. Rev. Lett. 100, 230404. 10.1103/PhysRevLett.100. 230404
7. Andrieux, D., P. Gaspard, S. Ciliberto, N. Garnier, S. Joubaud, and A. Petrosyan, 2007, " Entropy production and time asymmetry in nonequilibrium fluctuations, " Phys. Rev. Lett. 98, 150601. 10.1103/PhysRevLett.98.150601 (Pubitemid 46574384)
8. Andrieux, D., P. Gaspard, T. Monnai, and S. Tasaki, 2009, " Fluctuation theorem for currents in open quantum systems, " New J. Phys. 11, 043014. 10.1099/1367-2630/11/4/043014
9. Ben-Reuven, A., 1975, " Spectral line shapes in gases in the binary-collision approximation, " Adv. Chem. Phys. 33, 235. 10.1002/9780470142523.ch5
10. Bagrets, D. A., and Y. V. Nazarov, 2003, " Full counting statistics of charge transfer in Coulomb blockade systems, " Phys. Rev. B 67, 085316. 10.1103/PhysRevB.67.085316
11. Barkai, E., Y. Jung, and R. Silbey, 2004, " Theory of single-molecule spectroscopy: Beyond the ensemble average, " Annu. Rev. Phys. Chem. 55, 457. 10.1146/annurev.physchem.55.111803.143246
12. Bednorz, A., and W. Belzig, 2008, " Formulation of time-resolved counting statistics based on a positive-operator-valued measure, " Phys. Rev. Lett. 101, 206803. 10.1103/PhysRevLett.101.206803
13. Belzig, W., 2003, in Quantum Noise in Mesoscopic Physics, edited by, Y. V. Nazarov, NATO Science Series II: Mathematics, Physics and Chemistry Vol. 97 (Plenum, New York).
14. Belzig, W., and Y. V. Nazarov, 2001a, " Full counting statistics of electron transfer between superconductors, " Phys. Rev. Lett. 87, 197006. 10.1103/PhysRevLett.87.197006
15. Belzig, W., and Y. V. Nazarov, 2001b, " Full current statistics in diffusive normal-superconductor structures, " Phys. Rev. Lett. 87, 067006. 10.1103/PhysRevLett.87.067006
16. Blanter, Y. M., and M. Büttiker, 2000, " Shot noise in mesoscopic conductors, " Phys. Rep. 336, 1. 10.1016/S0370-1573(99)00123-4
17. Bochkov, G. N., and Y. E. Kuzovlev, 1977, " General theory of thermal fluctuations in nonlinear systems, " Zh. Eksp. Teor. Fiz. 72, 238
18. [Bochkov, G. N., and Y. E. Kuzovlev, Sov. Phys. JETP 45, 125 (1977)].
19. Bochkov, G. N., and Y. E. Kuzovlev, 1979, " Fluctuation-dissipation relations for nonequilibrium processes in open systems, " Zh. Eksp. Teor. Fiz. 76, 1071
20. [Bochkov, G. N., and Y. E. Kuzovlev, Sov. Phys. JETP 49, 543 (1979)].
21. Bochkov, G. N., and Y. E. Kuzovlev, 1981a, " Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. Generalized fluctuation-dissipation theorem, " Physica A 106, 443. 10.1016/0378-4371(81)90122-9
22. Bochkov, G. N., and Y. E. Kuzovlev, 1981b, " Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: II. Kinetic potential and variational principles for nonlinear irreversible processes, " Physica A 106, 480. 10.1016/0378-4371(81)90123-0
23. Braggio, A., J. König, and R. Fazio, 2006, " Full counting statistics in strongly interacting systems: Non-Markovian effects, " Phys. Rev. Lett. 96, 026805. 10.1103/PhysRevLett.96.026805 (Pubitemid 43248266)
24. Breuer, H. P., 2004, " Genuine quantum trajectories for non-Markovian processes, " Phys. Rev. A 70, 012106. 10.1103/PhysRevA.70. 012106
25. Breuer, H.-P., and F. Petruccione, 2002, The Theory of Open Quantum Systems (Oxford University Press, Oxford).
26. Brun, T. A., 2000, " Continuous measurements, quantum trajectories, and decoherent histories, " Phys. Rev. A 61, 042107. 10.1103/PhysRevA.61. 042107
27. Brun, T. A., 2002, " A simple model of quantum trajectories, " Am. J. Phys. 70, 719. 10.1119/1.1475328
28. Bylander, J., T. Duty, and P. Delsing, 2005, " Current measurement by real-time counting of single electrons, " Nature (London) 434, 361. 10.1038/nature03375 (Pubitemid 40469174)
29. Callen, H. B., and T. A. Welton, 1951, " Irreversibility and generalized noise, " Phys. Rev. 83, 34. 10.1103/PhysRev.83.34
30. Callens, I., W. De Roeck, T. Jacobs, C. Maes, and K. Netocny, 2004, " Quantum entropy production as a measure of irreversibility, " Physica D 187, 383. 10.1016/j.physd.2003.09.022
31. Campisi, M., 2008, " Complementary expressions for the entropy-from-work theorem, " Phys. Rev. E 78, 012102. 10.1103/PhysRevE.78. 012102
32. Cheng, Y. C., and R. J. Silbey, 2005, " Markovian approximation in the relaxation of open quantum systems, " J. Phys. Chem. B 109, 21399. 10.1021/jp051303o
33. Chernyak, V., and S. Mukamel, 2004, " Effect of quantum collapse on the distribution of work in driven single molecules, " Phys. Rev. Lett. 93, 048302. 10.1103/PhysRevLett.93.048302
34. Chernyak, V. Y., M. Chertkov, and C. Jarzynski, 2006, " Path-integral analysis of fluctuation theorems for general Langevin processes, " J. Stat. Mech.: Theory Exp. 2006, P08001. 10.1088/1742-5468/2006/08/ P08001 (Pubitemid 44525167)
35. Chetrite, R., and K. Gaȩdzki, 2008, " Fluctuation relations for diffusion processes, " Commun. Math. Phys. 282, 469. 10.1007/s00220-008-0502-9
36. Chou, K.-C., Z.-B. Su, B. L. Hao, and L. Yu, 1985, " Equilibrium and nonequilibrium formalisms made unified, " Phys. Rep. 118, 1. 10.1016/0370-1573(85)90136-X
37. Cleuren, B., and C. V. den Broeck, 2007, " Fluctuation theorem for black-body radiation, " EPL 79, 30001. 10.1209/0295-5075/79/30001
38. Cleuren, B., C. V. den Broeck, and R. Kawai, 2006, " Fluctuation and dissipation of work in a Joule experiment, " Phys. Rev. Lett. 96, 050601. 10.1103/PhysRevLett.96.050601 (Pubitemid 43270970)
39. Cohen, E. G. D., and G. Gallavotti, 1999, " Note on two theorems in nonequilibrium statistical mechanics, " e-print arXiv:cond-mat/9903418.
40. Cohen, E. G. D., and D. Mauzerall, 2004, " A note on the Jarzynski equality, " J. Stat. Mech.: Theory Exp. 2004, P07006. 10.1088/1742-5468/ 2004/07/P07006
41. Cohen-Tannoudji, C., J. Dupont-Roc, and G. Grynberg, 1996, Processus D'interaction Entre Photons et Atomes (CNRS Editions, Paris).
42. Collin, D., F. Ritort, C. Jarzynski, S. B. Smith, I. T. Tinoco, Jr., and C. Bustamante, 2005, " Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies, " Nature (London) 437, 231. 10.1038/nature04061 (Pubitemid 41294482)
43. Crooks, G. E., 1998, " Nonequilibrium measurement of free energy differences for microscopically reversible Markovian systems, " J. Stat. Phys. 90, 1481. 10.1023/A:1023208217925
44. Crooks, G. E., 1999, " Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, " Phys. Rev. E 60, 2721. 10.1103/PhysRevE.60.2721
45. Crooks, G. E., 2000, " Path-ensemble averages in systems driven far from equilibrium, " Phys. Rev. E 61, 2361. 10.1103/PhysRevE.61.2361
46. Crooks, G. E., 2008a, " On the Jarzynski relation for dissipative quantum dynamics, " J. Stat. Mech.: Theory Exp. 2008, P10023. 10.1088/1742-5468/2008/10/P10023
47. Crooks, G. E., 2008b, " Quantum operation time reversal, " Phys. Rev. A 77, 034101. 10.1103/PhysRevA.77.034101
48. de Groot, S. R., and P. Mazur, 1984, Non-equilibrium Thermodynamics (Dover, New York).
49. Derezinski, J., W. De Roeck, and C. Maes, 2008, " Fluctuations of quantum currents and unravelings of master equations, " J. Stat. Phys. 131, 341. 10.1007/s10955-008-9500-8
50. De Roeck, W., 2007, " Quantum fluctuation theorem: Can we go from micro to meso?, " C. R. Phys. 8, 674. 10.1016/j.crhy.2007.05.014
51. De Roeck, W., and C. Maes, 2004, " Quantum version of free-energy-irreversible-work relations, " Phys. Rev. E 69, 026115. 10.1103/PhysRevE.69.026115
52. De Roeck, W., and C. Maes, 2006, " Steady state fluctuations of the dissipated heat for a quantum stochastic model, " Rev. Math. Phys. 18, 619. 10.1142/S0129055X06002747 (Pubitemid 44412740)
53. Diósi, L., 2008, " Non-Markovian continuous quantum measurement of retarded observables, " Phys. Rev. Lett. 100, 080401. 10.1103/PhysRevLett.100.080401
54. Diósi, L., N. Gisin, and W. T. Strunz, 1998, " Non-Markovian quantum state diffusion, " Phys. Rev. A 58, 1699. 10.1103/PhysRevA.58.1699
55. Emary, C., D. Marcos, R. Aguado, and T. Brandes, 2007, " Frequency-dependent counting statistics in interacting nanoscale conductors, " Phys. Rev. B 76, 161404 (R). 10.1103/PhysRevB.76.161404
56. Engel, A., and R. Nolte, 2006, " Failure of the Jarzynski identity for a simple quantum system, " e-print arXiv:cond-mat/0612527.
57. Esposito, M., and P. Gaspard, 2003, " Quantum master equation for a system influencing its environment, " Phys. Rev. E 68, 066112. 10.1103/PhysRevE.68.066112
58. Esposito, M., and P. Gaspard, 2007, " Quantum master equation for the microcanonical ensemble, " Phys. Rev. E 76, 041134. 10.1103/PhysRevE.76.041134 (Pubitemid 350023341)
59. Esposito, M., U. Harbola, and S. Mukamel, 2007a, " Entropy fluctuation theorems for driven open systems: Application to electron counting statistics, " Phys. Rev. E 76, 031132. 10.1103/PhysRevE.76.031132 (Pubitemid 47507690)
60. Esposito, M., U. Harbola, and S. Mukamel, 2007b, " Fluctuation theorems for counting-statistics in electron transport through quantum junctions, " Phys. Rev. B 75, 155316. 10.1103/PhysRevB.75.155316
61. Esposito, M., and K. Lindenberg, 2008, " Continuous time random walk for open systems: Fluctuation theorems and counting statistics, " Phys. Rev. E 77, 051119. 10.1103/PhysRevE.77.051119 (Pubitemid 351718046)
62. Esposito, M., and S. Mukamel, 2006, " Fluctuation theorems for quantum master equations, " Phys. Rev. E 73, 046129. 10.1103/PhysRevE.73. 046129 (Pubitemid 43672790)
63. Evans, D. J., E. G. D. Cohen, and G. P. Morriss, 1993, " Probability of second law violations in shearing steady states, " Phys. Rev. Lett. 71, 2401. 10.1103/PhysRevLett.71.2401
64. Evans, D. J., and D. J. Searles, 1994, " Equilibrium microstates which generate second law violating steady states, " Phys. Rev. E 50, 1645. 10.1103/PhysRevE.50.1645
65. Evans, D. J., and D. J. Searles, 1995, " Steady states, invariant measures, and response theory, " Phys. Rev. E 52, 5839. 10.1103/PhysRevE.52.5839
66. Evans, D. J., and D. J. Searles, 1996, " Causality, response theory, and the second law of thermodynamics, " Phys. Rev. E 53, 5808. 10.1103/PhysRevE.53.5808
67. Fano, U., 1963, " Pressure broadening as a prototype of relaxation, " Phys. Rev. 131, 259. 10.1103/PhysRev.131.259
68. Feynman, R. P., and J. F. L. Vernon, 1963, " The theory of a general quantum system interacting with a linear dissipative system, " Ann. Phys. (N.Y.) 24, 118. 10.1016/0003-4916(63)90068-X
69. Flindt, C., T. Novotný, A. Braggio, M. Sassetti, and A. P. Jauho, 2008, " Counting statistics of non-Markovian quantum stochastic processes, " Phys. Rev. Lett. 100, 150601. 10.1103/PhysRevLett.100.150601 (Pubitemid 351561913)
70. Flindt, C., T. Novotny, and A.-P. Jauho, 2005, " Full counting statistics of nano-electromechanical systems, " Europhys. Lett. 69, 475. 10.1209/epl/i2004-10351-x (Pubitemid 40205262)
71. Förster, H., and M. Büttiker, 2008, " Fluctuation relations without microreversibility in nonlinear transport, " Phys. Rev. Lett. 101, 136805. 10.1103/PhysRevLett.101.136805
72. Fujisawa, T., T. Hayashi, and Y. H. H. D. Cheong, 2004, " Electron counting of single-electron tunneling current, " Appl. Phys. Lett. 84, 2343. 10.1063/1.1691491
73. Fujisawa, T., T. Hayashi, R. Tomita, and Y. Hirayama, 2006, " Bidirectional counting of single electrons, " Science 312, 1634. 10.1126/science.1126788 (Pubitemid 43902658)
74. Gallavotti, G., 1996a, " Chaotic hypothesis: Onsager reciprocity and fluctuation dissipation, " J. Stat. Phys. 84, 899. 10.1007/BF02174123
75. Gallavotti, G., 1996b, " Extension of Onsager's reciprocity to large fields and the chaotic hypothesis, " Phys. Rev. Lett. 77, 4334. 10.1103/PhysRevLett.77.4334
76. Gallavotti, G., 2007, " Fluctuation relation, fluctuation theorem, thermostats and entropy creation in non equilibrium statistical physics, " C. R. Phys. 8, 486. 10.1016/j.crhy.2007.04.011
77. Gallavotti, G., 2008, " Heat and fluctuations from order to chaos, " Eur. Phys. J. B 61, 1. 10.1140/epjb/e2008-00041-1 (Pubitemid 351198140)
78. Gallavotti, G., and E. G. D. Cohen, 1995a, " Dynamical ensembles in nonequilibrium statistical mechanics, " Phys. Rev. Lett. 74, 2694. 10.1103/PhysRevLett.74.2694
79. Gallavotti, G., and E. G. D. Cohen, 1995b, " Dynamical ensembles in stationary states, " J. Stat. Phys. 80, 931. 10.1007/BF02179860
80. Gambetta, J., and H. M. Wiseman, 2002, " Non-Markovian stochastic Schrödinger equations: Generalization to real-valued noise using quantum-measurement theory, " Phys. Rev. A 66, 012108. 10.1103/PhysRevA.66. 012108
81. Gambetta, J., and H. M. Wiseman, 2003, " Interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory, " Phys. Rev. A 68, 062104. 10.1103/PhysRevA.68.062104
82. Gardiner, C. W., and P. Zoller, 2000, Quantum Noise, 2nd ed. (Springer, New York).
83. Gaspard, P., 2004a, " Fluctuation theorem for nonequilibrium reactions, " J. Chem. Phys. 120, 8898. 10.1063/1.1688758
84. Gaspard, P., 2004b, " Time-reversed dynamical entropy and irreversibility in Markovian random processes, " J. Stat. Phys. 117, 599. 10.1007/s10955-004-3455-1 (Pubitemid 39436592)
85. Gaspard, P., 2006, " Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics, " Physica A 369, 201. 10.1016/j.physa.2006.04.010 (Pubitemid 43975250)
86. Gaspard, P., and M. Nagaoka, 1999a, " Non-Markovian stochastic Schrödinger equation, " J. Chem. Phys. 111, 5676. 10.1063/1.479868
87. Gaspard, P., and M. Nagaoka, 1999b, " Slippage of initial conditions for the Redfield master equation, " J. Chem. Phys. 111, 5668. 10.1063/1.479867
88. Gelin, M. F., and D. S. Kosov, 2008, " Unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems, " Phys. Rev. E 78, 011116. 10.1103/PhysRevE.78.011116
89. Glauber, R. J., 1963, " Coherent and incoherent states of the radiation field, " Phys. Rev. 131, 2766. 10.1103/PhysRev.131.2766
90. Gomez-Marin, A., J. M. R. Parrondo, and C. V. den Broeck, 2008, " The 'footprints' of irreversibility, " EPL 82, 50002. 10.1209/0295-5075/82/ 50002
91. Gurvitz, S. A., 1997, " Measurements with a noninvasive detector and dephasing mechanism, " Phys. Rev. B 56, 15215. 10.1103/PhysRevB.56.15215
92. Gustavsson, S., R. Leturcq, B. Simovic, R. Schleser, T. Ihn, P. Studerus, K. Ensslin, D. C. Driscol, and A. C. Gossard, 2006, " Counting statistics of single electron transport in a quantum dot, " Phys. Rev. Lett. 96, 076605. 10.1103/PhysRevLett.96.076605 (Pubitemid 43297045)
93. Harbola, U., M. Esposito, and S. Mukamel, 2006, " Quantum master equation for electron transport through quantum dots and single molecules, " Phys. Rev. B 74, 235309. 10.1103/PhysRevB.74.235309 (Pubitemid 44879193)
94. Harbola, U., M. Esposito, and S. Mukamel, 2007, " Statistics and fluctuation theorem for boson and fermion transport through mesoscopic junctions, " Phys. Rev. B 76, 085408. 10.1103/PhysRevB.76.085408
95. Harbola, U., and S. Mukamel, 2006, " Nonequilibrium superoperator GW equations, " J. Chem. Phys. 124, 044106. 10.1063/1.2161177 (Pubitemid 43166304)
96. Harbola, U., and S. Mukamel, 2008, " Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions, " Phys. Rep. 465, 191. 10.1016/j.physrep.2008.05.003
97. Harris, R. J., and G. M. Schutz, 2007, " Fluctuation theorems for stochastic dynamics, " J. Stat. Mech.: Theory Exp. 2007, P07020. 10.1088/1742-5468/2007/07/P07020
98. Hatano, T., and S. I. Sasa, 2001, " Steady-state thermodynamics of Langevin systems, " Phys. Rev. Lett. 86, 3463. 10.1103/PhysRevLett.86.3463 (Pubitemid 32416153)
99. Horowitz, J., and C. Jarzynski, 2007, " Comparison of work fluctuation relations, " J. Stat. Mech.: Theory Exp. 2007, P11002. 10.1088/1742-5468/2007/11/P11002
100. Jarzynski, C., 1997a, " Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, " Phys. Rev. E 56, 5018. 10.1103/PhysRevE.56.5018
101. Jarzynski, C., 1997b, " Nonequilibrium equality for free energy differences, " Phys. Rev. Lett. 78, 2690. 10.1103/PhysRevLett.78.2690
102. Jarzynski, C., 2004, " Nonequilibrium work theorem for a system strongly coupled to a thermal environment, " J. Stat. Mech.: Theory Exp. 2004, P09005. 10.1088/1742-5468/2004/09/P09005
103. Jarzynski, C., 2007, " Comparison of far-from-equilibrium work relations, " C. R. Phys. 8, 495. 10.1016/j.crhy.2007.04.010
104. Jarzynski, C., and D. K. Wojcik, 2004, " Classical and quantum fluctuation theorems for heat exchange, " Phys. Rev. Lett. 92, 230602. 10.1103/PhysRevLett.92.230602
105. Jordan, A. N., E. V. Sukhorukov, and S. Pilgram, 2004, " Fluctuation statistics in networks: A stochastic path integral approach, " J. Tech. Phys. 45, 4386.
106. Jordan, T. F., A. Shaji, and E. C. G. Sudarshan, 2008, " Markov approximations encounter map domains: A hazard of open quantum dynamics, " Phys. Rev. A 77, 032104. 10.1103/PhysRevA.77.032104
107. Kamenev, A., 2002, " Keldysh and Doi-Peliti techniques for out-of-equilibrium systems, " in Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems, edited by, I. V. Lerner, B. L. Altshuler, V. I. Fal'ko, and, T. Giamarchi, NATO Science Series II (Kluwer, Dordrecht), Vol. 72.
108. Kawai, R., J. M. R. Parrondo, and C. V. den Broeck, 2007, " Dissipation: The phase-space perspective, " Phys. Rev. Lett. 98, 080602. 10.1103/PhysRevLett.98.080602 (Pubitemid 46326134)
109. Kelley, P. L., and W. H. Kleiner, 1964, " Theory of electromagnetic field measurement and photoelectron counting, " Phys. Rev. 136, A316. 10.1103/PhysRev.136.A316
110. Kiesslich, G., P. Samuelsson, A. Wacker, and E. Schöll, 2006, " Counting statistics and decoherence in coupled quantum dots, " Phys. Rev. B 73, 033312. 10.1103/PhysRevB.73.033312 (Pubitemid 43270564)
111. Kindermann, M., and Y. V. Nazarov, 2003, " Full counting statistics in electric circuit, " in Quantum Noise in Mesoscopic Physics, edited by, Y. V. Nazarov, NATO ASI Science Series (Kluwer Academic, Dordrecht).
112. Kindermann, M., and S. Pilgram, 2004, " Statistics of heat transfer in mesocopic circuits, " Phys. Rev. B 69, 155334. 10.1103/PhysRevB.69. 155334
113. Kohen, D., C. C. Marston, and D. J. Tannor, 1997, " Phase space approach to theories of quantum dissipation, " J. Chem. Phys. 107, 5236. 10.1063/1.474887
114. Kondepudi, D., and I. Prigogine, 1998, Modern Thermodynamics (Wiley, New York).
115. Kubo, R., 1957, " Statistical-mechanical theory of irreversible processes. I., " J. Phys. Soc. Jpn. 12, 570. 10.1143/JPSJ.12.570
116. Kubo, R., M. Toda, and N. Hashitsume, 1998, Statistical Physics II: Nonequilibrium Statistical Mechanics, 2nd ed. (Springer, New York).
117. Kullback, S., and R. A. Leibler, 1951, " On information and sufficiency, " Ann. Math. Stat. 22, 79. 10.1214/aoms/1177729694
118. Kulzer, F., and M. Orrit, 2004, " Single-molecule optics, " Annu. Rev. Phys. Chem. 55, 585. 10.1146/annurev.physchem.54.011002.103816
119. Kurchan, J., 1998, " Fluctuation theorem for stochastic dynamics, " J. Phys. A 31, 3719. 10.1088/0305-4470/31/16/003 (Pubitemid 128059972)
120. Kurchan, J., 2000, " A quantum fluctuation theorem, " e-print arXiv:cond-mat/0007360.
121. Lebowitz, J. L., and H. Spohn, 1999, " A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, " J. Stat. Phys. 95, 333. 10.1023/A:1004589714161
122. Lechner, W., and C. Dellago, 2007, " On the efficiency of path sampling methods for the calculation of free energies from non-equilibrium simulations, " J. Stat. Mech.: Theory Exp. 2007, P04001. 10.1088/1742-5468/2007/04/P04001
123. Lechner W., H. Oberhofer, C. Dellago, and P. L. Geissler, 2006, " Equilibrium free energies from fast-switching trajectories with large time steps, " J. Chem. Phys. 124, 044113. 10.1063/1.2162874 (Pubitemid 43166310)
124. Levitov, L. S., H. Lee, and G. B. Lesovik, 1996, " Electron counting statistics and coherent states of electric current, " J. Math. Phys. 37, 4845. 10.1063/1.531672
125. Levitov, L. S., and G. B. Lesovik, 1993, " Charge distribution in quantum shot noise, " JETP Lett. 58, 230.
126. Levitov, L. S., and M. Reznikov, 2004, " Counting statistics of tunneling current, " Phys. Rev. B 70, 115305. 10.1103/PhysRevB.70.115305
127. Lindblad, G., 1976, " On the generators of quantum dynamical semigroups, " Commun. Math. Phys. 48, 119. 10.1007/BF01608499
128. Liphardt, J., S. Dumont, S. B. Smith, I. T. (Jr), and C. Bustamante, 2002, " Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality, " Science 296, 1832. 10.1126/science.1071152 (Pubitemid 34596263)
129. Lu, W., Z. Ji, L. Pfeiffer, K. W. West, and A. J. Rimberg, 2003, " Real-time detection of electron tunnelling in a quantum dot, " Nature (London) 423, 422. 10.1038/nature01642 (Pubitemid 36626990)
130. Maes, C., 2003, " On the origin and the use of fluctuation relation for the entropy, " Séminaire Poincaré 2, 29.
131. Mandel, L., 1982, " Squeezed states and sub-Poissonian photon statistics, " Phys. Rev. Lett. 49, 136. 10.1103/PhysRevLett.49.136
132. Mandel, L., and E. Wolf, 1995, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge).
133. Mehta, P., and N. Andrei, 2008, " Nonequilibrium quantum impurities: From entropy production to information theory, " Phys. Rev. Lett. 100, 086804. 10.1103/PhysRevLett.100.086804
134. Merzbacher, E., 1970, Quantum Mechanics, 2nd ed. (Wiley, New York).
135. Monnai, T., 2005, " Unified treatment of the quantum fluctuation theorem and the Jarzynski equality in terms of microscopic reversibility, " Phys. Rev. E 72, 027102. 10.1103/PhysRevE.72.027102 (Pubitemid 41520829)
136. Monnai, T., and S. Tasaki, 2003, " Quantum correction of fluctuation theorem, " e-print arXiv:cond-mat/0308337.
137. Mukamel, S., 1995, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, Oxford).
138. Mukamel, S., 2003a, " Photon statistics: Nonlinear spectroscopy of single quantum systems, " Phys. Rev. A 68, 063821. 10.1103/PhysRevA.68. 063821
139. Mukamel, S., 2003b, " Quantum extension of the Jarzynski relation: Analogy with stochastic dephasing, " Phys. Rev. Lett. 90, 170604. 10.1103/PhysRevLett.90.170604
140. Nagaev, K. E., S. Pilgram, and M. Büttiker, 2004, " Frequency scales for current statistics of mesoscopic conductors, " Phys. Rev. Lett. 92, 176804. 10.1103/PhysRevLett.92.176804
141. Nazarov, Y. V., 1999, " Universalities of weak localisation, " Ann. Phys. 8, SI193.
142. Nazarov, Y. V., 2007, " Full counting statistics and field theory, " Ann. Phys. 16, 720. 10.1002/andp.200710259 (Pubitemid 350075347)
143. Nazarov, Y. V., and M. Kindermann, 2003, " Full counting statistics of a general quantum mechanical variable, " Eur. Phys. J. B 35, 413. 10.1140/epjb/e2003-00293-1 (Pubitemid 41200982)
144. Negele, J., and H. Orland, 1998, Quantum Many Particle Physics (Westview Press, Boulder, CO).
145. Nielsen, M. A., and I. Chuang, 2000, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge).
146. Pechukas, P., 1994, " Reduced dynamics need not be completely positive, " Phys. Rev. Lett. 73, 1060. 10.1103/PhysRevLett.73.1060
147. Pilgram, S., 2004, " Electron-electron scattering effects on the full counting statistics of mesoscopic conductors, " Phys. Rev. B 69, 115315. 10.1103/PhysRevB.69.115315
148. Pilgram, S., A. N. Jordan, E. Sukhorukov, and M. Büttiker, 2003, " Stochastic path integral formulation of full counting statistics, " Phys. Rev. Lett. 90, 206801. 10.1103/PhysRevLett.90.206801
149. Pilgram, S., K. E. Nagaev, and M. Büttiker, 2004, " Frequency-dependent third cumulant of current in diffusive conductors, " Phys. Rev. B 70, 045304. 10.1103/PhysRevB.70.045304
150. Pilgram, S., P. Samuelsson, H. Förster, and M. Büttiker, 2006, " Full-counting statistics for voltage and dephasing probes, " Phys. Rev. Lett. 97, 066801. 10.1103/PhysRevLett.97.066801 (Pubitemid 44215648)
151. Plenio, M. B., and P. L. Knight, 1998, " The quantum-jump approach to dissipative dynamics in quantum optics, " Rev. Mod. Phys. 70, 101. 10.1103/RevModPhys.70.101 (Pubitemid 128022010)
152. Rammer, J., A. L. Shelankov, and J. Wabnig, 2004, " Quantum measurement in charge representation, " Phys. Rev. B 70, 115327. 10.1103/PhysRevB.70.115327
153. Ross, J., K. L. C. Hunt, and P. M. Hunt, 1988, " Thermodynamics far from equilibrium: Reactions with multiple stationary states, " J. Chem. Phys. 88, 2719. 10.1063/1.454002
154. Saito, K., and A. Dhar, 2007, " Fluctuation theorem in quantum heat conduction, " Phys. Rev. Lett. 99, 180601. 10.1103/PhysRevLett.99.180601 (Pubitemid 350074470)
155. Saito, K., and Y. Utsumi, 2008, " Symmetry in full counting statistics, fluctuation theorem, and relations among nonlinear transport coefficients in the presence of a magnetic field, " Phys. Rev. B 78, 115429. 10.1103/PhysRevB.78.115429
156. Sanda, F., and S. Mukamel, 2005, " Liouville-space pathways for spectral diffusion in photon statistics from single molecules, " Phys. Rev. A 71, 033807. 10.1103/PhysRevA.71.033807
157. Schaller, G., and T. Brandes, 2008, " Preservation of positivity by dynamical coarse-graining, " Phys. Rev. A 78, 022106. 10.1103/PhysRevA.78. 022106
158. Schöll-Paschinger, E., and C. Dellago, 2006, " A proof of Jarzynskis nonequilibrium work theorem for dynamical systems that conserve the canonical distribution, " J. Chem. Phys. 125, 054105. 10.1063/1.2227025 (Pubitemid 44188395)
159. Schönhammer, K., 2007, " Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula, " Phys. Rev. B 75, 205329. 10.1103/PhysRevB.75.205329
160. Schuler, S., T. Speck, C. Tietz, J. Wrachtrup, and U. Seifert, 2005, " Experimental test of the fluctuation theorem for a driven two-level system with time-dependent rates, " Phys. Rev. Lett. 94, 180602. 10.1103/PhysRevLett.94.180602 (Pubitemid 41493029)
161. Searles, D. J., and D. J. Evans, 1999, " Fluctuation theorem for stochastic systems, " Phys. Rev. E 60, 159. 10.1103/PhysRevE.60.159
162. Segal, D., and A. Nitzan, 2005, " Spin-boson thermal rectifier, " Phys. Rev. Lett. 94, 034301. 10.1103/PhysRevLett.94.034301 (Pubitemid 40607293)
163. Seifert, U., 2005, " Entropy production along a stochastic trajectory and an integral fluctuation theorem, " Phys. Rev. Lett. 95, 040602. 10.1103/PhysRevLett.95.040602 (Pubitemid 41506195)
164. Shelankov, A., and J. Rammer, 2003, " Charge transfer counting statistics revisited, " EPL 63, 485. 10.1209/epl/i2003-00567-2 (Pubitemid 37052701)
165. Snyman, I., and Y. V. Nazarov, 2008, " The Keldysh action of a multi-terminal time-dependent scatterer, " Phys. Rev. B 77, 165118. 10.1103/PhysRevB.77.165118
166. Sornette, D., 2006, Critical Phenomena in Natural Sciences, 2nd ed. (Springer, New York).
167. Spohn, H., 1980, " Kinetic equations from Hamiltonian dynamics: Markovian limits, " Rev. Mod. Phys. 52, 569. 10.1103/RevModPhys.52.569
168. Stratonovich, R. L., 1992, Nonlinear Nonequilibrium Thermodynamics I (Springer, New York).
169. Stratonovich, R. L., 1994, Nonlinear Nonequilibrium Thermodynamics II (Springer, New York).
170. Strunz, W. T., 1996, " Linear quantum state diffusion for non-Markovian open quantum systems, " Phys. Lett. A 224, 25. 10.1016/S0375-9601(96)00805-5
171. Strunz, W. T., L. Diósi, and N. Gisin, 1999, " Open system dynamics with non-Markovian quantum trajectories, " Phys. Rev. Lett. 82, 1801. 10.1103/PhysRevLett.82.1801
172. Suarez, A., R. Silbey, and I. Oppenheim, 1992, " Memory effects in the relaxation of quantum open systems, " J. Chem. Phys. 97, 5101. 10.1063/1.463831
173. Talkner, P., P. S. Burada, and P. Hänggi, 2008, " Statistics of work performed on a forced quantum oscillator, " Phys. Rev. E 78, 011115; 10.1103/PhysRevE.78.011115
174. Talkner, P., P. S. Burada, and P. Hänggi, " Erratum: Statistics of work performed on a forced quantum oscillator, " Phys. Rev. E 79, 039902 (E) (2009). 10.1103/PhysRevE.79.039902
175. Talkner, P., M. Campisi, and P. Hänggi, 2009, " Fluctuation theorems in driven open quantum systems, " J. Stat. Mech.: Theory Exp. 2009, P02025. 10.1088/1742-5468/2009/02/P02025
176. Talkner, P., and P. Hänggi, 2007, " The Tasaki-Crooks quantum fluctuation theorem, " J. Phys. A: Math. Theor. 40, F569. 10.1088/1751-8113/40/26/F08
177. Talkner, P., P. Hänggi, and M. Morillo, 2008, " A microcanonical quantum fluctuation theorem, " Phys. Rev. E 77, 051131. 10.1103/PhysRevE.77.051131
178. Talkner, P., E. Lutz, and P. Hänggi, 2007, " Fluctuation theorems: Work is not an observable, " Phys. Rev. E 75, 050102 (R). 10.1103/PhysRevE.75.050102 (Pubitemid 47000998)
179. Taniguchi, T., and E. G. D. Cohen, 2007, " Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems, " J. Stat. Phys. 126, 1. 10.1007/s10955-006-9252-2
180. Tasaki, H., 2000, " Jarzynski relations for quantum systems and some applications, " e-print arXiv:cond-mat/0009244.
181. Tietz, C., S. Schuler, T. Speck, U. Seifert, and J. Wrachtrup, 2006, " Measurement of stochastic entropy production, " Phys. Rev. Lett. 97, 050602. 10.1103/PhysRevLett.97.050602 (Pubitemid 44157405)
182. Tobiska, J., and Y. V. Nazarov, 2005, " Inelastic interaction corrections and universal relations for full counting statistics in a quantum contact, " Phys. Rev. B 72, 235328. 10.1103/PhysRevB.72.235328 (Pubitemid 43029144)
183. Touchette, H., 2009, " The large deviation approach to statistical mechanics, " Phys. Rep. 478, 1. 10.1016/j.physrep.2009.05.002
184. Trepagnier, E. H., C. Jarzynski, F. Ritort, G. E. Crooks, C. J. Bustamante, and J. Liphardt, 2004, " Experimental test of Hatano and Sasas nonequilibrium steady-state equality, " Proc. Natl. Acad. Sci. U.S.A. 101, 15038. 10.1073/pnas.0406405101 (Pubitemid 39391714)
185. Utsumi, Y., D. S. Golubev, and G. Schön, 2006, " Full counting statistics for a single-electron transistor: Nonequilibrium effects at intermediate conductance, " Phys. Rev. Lett. 96, 086803. 10.1103/PhysRevLett.96.086803 (Pubitemid 43306895)
186. Utsumi, Y., and K. Saito, 2009, " Fluctuation theorem in a quantum-dot Aharonov-Bohm interferometer, " Phys. Rev. B 79, 235311. 10.1103/PhysRevB.79.235311
187. Vaikuntanathan, S., and C. Jarzynski, 2008, " Escorted free energy simulations: Improving convergence by reducing dissipation, " Phys. Rev. Lett. 100, 190601. 10.1103/PhysRevLett.100.190601 (Pubitemid 351705647)
188. van Kampen, N. G., 1997, Stochastic Processes in Physics and Chemistry, 2nd ed. (North-Holland, Amsterdam).
189. van Zon, R., and E. G. D. Cohen, 2003, " Extension of the fluctuation theorem, " Phys. Rev. Lett. 91, 110601. 10.1103/PhysRevLett.91. 110601
190. van Zon, R., and E. G. D. Cohen, 2004, " Extended heat-fluctuation theorems for a system with deterministic and stochastic forces, " Phys. Rev. E 69, 056121. 10.1103/PhysRevE.69.056121
191. Wabnig, J., D. V. Khomitsky, J. Rammer, and A. L. Shelankov, 2005, " Statistics of charge transfer in a tunnel junction coupled to an oscillator, " Phys. Rev. B 72, 165347. 10.1103/PhysRevB.72.165347 (Pubitemid 43022047)
192. Wang, E., and U. Heinz, 2002, " Generalized fluctuation-dissipation theorem for nonlinear response functions, " Phys. Rev. D 66, 025008. 10.1103/PhysRevD.66.025008
193. Wang, G. M., J. C. Reid, D. M. Carberry, D. R. M. Williams, E. M. Sevick, and D. J. Evans, 2005, " Experimental study of the fluctuation theorem in a nonequilibrium steady state, " Phys. Rev. E 71, 046142. 10.1103/PhysRevE.71.046142
194. Warszawski, P., and H. M. Wiseman, 2003a, " Quantum trajectories for realistic photodetection: I. General formalism, " J. Opt. B: Quantum Semiclassical Opt. 5, 1. 10.1088/1464-4266/5/1/301
195. Warszawski, P., and H. M. Wiseman, 2003b, " Quantum trajectories for realistic photodetection: II. Application and analysis, " J. Opt. B: Quantum Semiclassical Opt. 5, 15. 10.1088/1464-4266/5/1/302
196. Welack, S., M. Esposito, U. Harbola, and S. Mukamel, 2008, " Interference effects in the counting statistics of electron transfers through a double quantum dot, " Phys. Rev. B 77, 195315. 10.1103/PhysRevB.77.195315
197. Wigner, E. P., 1960, " Normal form of antiunitary operators, " J. Math. Phys. 1, 409. 10.1063/1.1703672
198. Wiseman, H. M., and G. J. Milburn, 1993a, " Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere, " Phys. Rev. A 47, 1652. 10.1103/PhysRevA.47.1652
199. Wiseman, H. M., and G. J. Milburn, 1993b, " Quantum theory of field-quadrature measurements, " Phys. Rev. A 47, 642. 10.1103/PhysRevA.47. 642
200. Yacobs, T., and C. Maes, 2005, " Reversibility and irreversibility within the quantum formalism, " Phys. Mag. 27, 119.
201. Yukawa, S., 2000, " A quantum analogue of the Jarzynski equality, " J. Phys. Soc. Jpn. 69, 2367. 10.1143/JPSJ.69.2367
202. Zheng, Y., and F. L. H. Brown, 2003a, " Photon emission from driven single molecules, " J. Chem. Phys. 119, 11814. 10.1063/1.1623484
203. Zheng, Y., and F. L. H. Brown, 2003b, " Single-molecule photon counting statistics via generalized optical Bloch equations, " Phys. Rev. Lett. 90, 238305. 10.1103/PhysRevLett.90.238305
204. Zwanzig, R., 2001, Nonequilibrium Statistical Mechanics (Oxford University Press, Oxford).