Time-Reversal Symmetry Relations for Currents in Quantum and Stochastic Nonequilibrium Systems

Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond

Volumn , Issue , 2013, Pages 213-257

  Gaspard, Pierre ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Affinity; Current fluctuation theorem; Full counting statistics; Mesoscopic electronic circuits; Microreversibility; Nonequilibrium statistical mechanics; Quantum transport; Response theory; Thermodynamic entropy production

Indexed keywords

EID: 84885503404     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527658701.ch7     Document Type: Chapter

References (119)

1. Imry, Y. (1997) Introduction to Mesoscopic Physics, Oxford University Press, New York.
2. Ferry, D.K., Goodnick, S.M., and Bird, J. (2009) Transport in Nanostructures, 2nd edn., Cambridge University Press, Cambridge, UK.
3. Nazarov, Y.V. and Blanter, Y.M. (2009) Quantum Transport, Cambridge University Press, Cambridge, UK.
4. Gaspard, P. (2006) Physica A, 369, 201.
5. Balescu, R. (1975) Equilibrium and Nonequilibrium Statistical Mechanics, John Wiley & Sons, Inc., New York.
6. Eckmann, J.-P. and Ruelle, D. (1985) Rev. Mod. Phys., 57, 617.
7. Posch, H.A. and Hoover,W.G. (1988) Phys. Rev. A, 38, 473.
8. Gaspard, P. and Nicolis, G. (1990) Phys. Rev. Lett., 65, 1693.
9. Gaspard, P. and Baras, F. (1995) Phys. Rev. E, 51, 5332.
10. Dorfman, J.R. and Gaspard, P. (1995) Phys. Rev. E, 51, 28.
11. Gaspard, P. and Dorfman, J.R. (1995) Phys. Rev. E, 52, 3525.
12. van Beijeren, H., Dorfman, J.R., Posch, H.A., and Dellago, Ch. (1997) Phys. Rev. E, 56, 5272.
13. Gaspard, P. (1998) Chaos, Scattering and Statistical Mechanics, Cambridge University Press, Cambridge, UK.
14. Dorfman, J.R. (1999) An Introduction to Chaos in Nonequilibrium Statistical Mechanics, Cambridge University Press, Cambridge, UK.
15. Gaspard, P., Claus, I., Gilbert, T., and Dorfman, J.R. (2001) Phys. Rev. Lett., 86, 1506.
16. Klages, R. (2007) Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics, World Scientific, Singapore.
17. Evans, D.J. and Morriss, G.P. (2008) Statistical Mechanics of Nonequilibrium Liquids, 2nd edn, Cambridge University Press, Cambridge, UK.
18. Collin, D., Ritort, F., Jarzynski, C., Smith, S.B., Tinoco, I., Jr., and Bustamante, C. (2005) Nature, 437, 231.
19. Lussis, P., Svaldo-Lanero, T., Bertocco, A., Fustin, C.-A., Leigh, D.A., and Duwez, A.-S. (2011) Nat. Nanotechnol., 6, 553.
20. Jarzynski, C. (1997) Phys. Rev. Lett., 78, 2690.
21. Crooks, G.E. (1998) J. Stat. Phys., 90, 1481.
22. Crooks, G.E. (1999) Phys. Rev. E, 60, 2721.
23. Jarzynski, C. (2000) J. Stat. Phys., 98, 77.
24. Evans, D.J., Cohen, E.G.D., and Morriss, G.P. (1993) Phys. Rev. Lett., 71, 2401.
25. Gallavotti, G. and Cohen, E.G.D. (1995) Phys. Rev. Lett., 74, 2694.
26. Gallavotti, G. (1996) Phys. Rev. Lett., 77, 4334.
27. Kurchan, J. (1998) J. Phys. A, 31, 3719.
28. Lebowitz, J.L. and Spohn, H. (1999) J. Stat. Phys., 95, 333.
29. Maes, C. (1999) J. Stat. Phys., 95, 367.
30. Evans, D.J. and Searles, D.J. (2002) Adv. Phys., 51, 1529.
31. van Zon, R. and Cohen, E.G.D. (2003) Phys. Rev. E, 67, 046102.
32. Altland, A., De Martino, A., Egger, R., and Narozhny, B. (2010) Phys. Rev. B, 82, 115323.
33. Mallick, K., Moshe, M., and Orland, H. (2011) J. Phys. A, 44, 095002.
34. Jarzynski, C. (2011) Annu. Rev. Condens. Matter Phys., 2, 329.
35. Maes, C. and Netočná, K. (2003) J. Stat. Phys., 110, 269.
36. Gaspard, P. (2004) J. Stat. Phys., 117, 599.
37. Gaspard, P. (2005) New J. Phys., 7, 77.
38. Kawai, R., Parrondo, J.M.R., and Van den Broeck, C. (2007) Phys. Rev. Lett., 98, 080602.
39. Gaspard, P. (2007) C. R. Phys., 8, 598.
40. Andrieux, D., Gaspard, P., Ciliberto, S., Garnier, N., Joubaud, S., and Petrosyan, A. (2007) Phys. Rev. Lett., 98, 150601.
41. Andrieux, D., Gaspard, P., Ciliberto, S., Garnier, N., Joubaud, S., and Petrosyan, A. (2008) J. Stat. Mech., P01002.
42. Callen, I., De Roeck,W., Jacob, T., Maes, C., and Netočný, K. (2004) Physica D, 187, 383.
43. Mukamel, S. (2003) Phys. Rev. Lett., 90, 170604.
44. Tobiska, J. and Nazarov, Yu.V. (2005) Phys. Rev. B, 72, 235328.
45. Esposito, M., Harbola, U., and Mukamel, S. (2007) Phys. Rev. B, 75, 155316.
46. Harbola, U., Esposito, M., and Mukamel, S. (2007) Phys. Rev. B, 76, 085408.
47. Saito, K. and Utsumi, Y. (2008) Phys. Rev. B, 78, 115429.
48. Andrieux, D. and Gaspard, P. (2008) Phys. Rev. Lett., 100, 230404.
49. Andrieux, D., Gaspard, P., Monnai, T., and Tasaki, S. (2009) New J. Phys., 11, 043014(Erratum, ibid., p. 109802).
50. Saito, K. and Dhar, A. (2007) Phys. Rev. Lett., 99, 180601.
51. Talkner, P. and Hänggi, P. (2007) J. Phys. A, 40, F569.
52. Talkner, P., Lutz, E., and Hänggi, P. (2007) Phys. Rev. E, 75, 050102.
53. Campisi, M., Hänggi, P., and Talkner, P. (2011) Rev. Mod. Phys., 83, 771 (Erratum, ibid., p. 1653).
54. Gelin, M.F. and Kosov, D.S. (2008) Phys. Rev. E, 78, 011116.
55. Esposito, M., Harbola, U., and Mukamel, S. (2009) Rev. Mod. Phys., 81, 1665.
56. Gustavsson, S., Leturcq, R., Simovi9c, B., Schleser, R., Ihn, T., Studerus, P., Ensslin, K., Driscoll, D.C., and Gossard, A.C. (2006) Phys. Rev. Lett., 96, 076605.
57. Gustavsson, S., Leturcq, R., Studer, M., Shorubalko, I., Ihn, T., Ensslin, K., Driscoll, D.C., and Gossard, A.C. (2009) Surf. Sci. Rep., 64, 191.
58. Fujisawa, T., Hayashi, T., Tomita, R., and Hirayama, Y. (2006) Science, 312, 1634.
59. Utsumi, Y., Golubev, D.S., Marthaler, M., Saito, K., Fujisawa, T., and Schön, G. (2010) Phys. Rev. B, 81, 125331.
60. Küng, B., Rössler, C., Beck, M., Marthaler, M., Golubev, D.S., Utsumi, Y., Ihn, T., and Ensslin, K. (2012) Phys. Rev. X, 2, 011001.
61. Nakamura, S., Yamauchi, Y., Hashisaka, M., Chida, K., Kobayashi, K., Ono, T., Leturcq, R., Ensslin, K., Saito, K., Utsumi, Y., and Gossard, A.C. (2010) Phys. Rev. Lett., 104, 080602.
62. Nakamura, S., Yamauchi, Y., Hashisaka, M., Chida, K., Kobayashi, K., Ono, T., Leturcq, R., Ensslin, K., Saito, K., Utsumi, Y., and Gossard, A.C. (2011) Phys. Rev. B, 83, 155431.
63. Bochkov, G.N. and Kuzovlev, Yu.E. (1977) Sov. Phys., 45, 125.
64. Stratonovich, R.L. (1994) Nonlinear Nonequilibrium Thermodynamics II: Advanced Theory, Springer, Berlin.
65. Kubo, R. (1957) J. Phys. Soc. Jpn., 12, 570.
66. Onsager, L. (1931) Phys. Rev., 37, 405.
67. Casimir, H.B.G. (1945) Rev. Mod. Phys., 17, 343.
68. Tasaki, S. (2001) Chaos Soliton Fract., 12, 2657.
69. Tasaki, S. and Matsui, T. (2003) Fundamental Aspects of Quantum Physics (eds L. Accardi and S. Tasaki), World Scientific, New Jersey, pp. 100-119.
70. Tasaki, S. and Takahashi, J. (2006) Prog. Theor. Phys. Suppl., 165, 57.
71. De Donder, T. and Van Rysselberghe, P. (1936) Affinity, Stanford University Press, Menlo Park, CA.
72. Prigogine, I. (1967) Introduction to Thermodynamics of Irreversible Processes, John Wiley & Sons, Inc., New York.
73. Callen, H.B. (1985) Thermodynamics and an Introduction to Thermostatistics, John Wiley & Sons, Inc., NewYork.
74. Andrieux, D. and Gaspard, P. (2004) J. Chem. Phys., 121, 6167.
75. Andrieux, D. and Gaspard, P. (2006) J. Stat. Mech., P01011.
76. Andrieux, D. and Gaspard, P. (2007) J. Stat. Mech., P02006.
77. Gaspard, P., Alonso, D., Okuda, T., and Nakamura, K. (1994) Phys. Rev. E, 50, 2591.
78. Nakamura, K. and Harayama, T. (2004) Quantum Chaos and Quantum Dots, Oxford University Press, Oxford.
79. Büttiker, M. (1990) Phys. Rev. B, 41, 7906.
80. Klich, I. (2003) Quantum Noise in Mesoscopic Physics (ed. Y.V. Nazarov), Kluwer, Dordrecht.
81. Avron, J.E., Bachmann, S., Graff, G.M., and Klich, I. (2008) Commun. Math. Phys., 280, 807.
82. Levitov, L.S. and Lesovik, G.B. (1993) JETP Lett., 58, 230.
83. Levitov, L.S., Lee, H.W., and Lesovik, G. B. (1996) J. Math. Phys., 37, 4845.
84. Roche, P.-E., Derrida, B., and DouScot, B. (2005) Eur. Phys. J. B, 43, 529.
85. Sivan, U. and Imry, Y. (1986) Phys. Rev. B, 33, 551.
86. Takahashi, J. and Tasaki, S. (2005) J. Phys. Soc. Jpn Suppl., 74, 261.
87. Blanter, Y.M. and Büttiker, M. (2000) Phys. Rep., 336, 1.
88. van Wees, B.J., van Houten, H., Beenakker, C.W.J., Williamson, J.G., Kouwenhoven, L.P., van der Marel, D., and Foxon, C.T. (1988) Phys. Rev. Lett., 60, 848.
89. Rammer, J. (2007) Quantum Field Theory of Non-Equilibrium States, Cambridge University Press, Cambridge, UK.
90. Mukamel, S. (1995) Principles of Nonlinear Optical Spectroscopy, Oxford University Press, Oxford.
91. Harbola, U. and Mukamel, S. (2008) Phys. Rep., 465, 191.
92. Umezawa, H., Matsumoto, H., and Tachiki, M. (1982) Thermo Field Dynamics and Condensed States, North-Holland, Amsterdam.
93. Kosov, D.S. (2009) J. Chem. Phys., 131, 171102.
94. Dzhioev, A.A. and Kosov, D.S. (2011) J. Chem. Phys., 134, 044121.
95. Gaspard, P. and Nagaoka, M. (1999) J. Chem. Phys., 111, 5668.
96. Gaspard, P. and Nagaoka, M. (1999) J. Chem. Phys., 111, 5676.
97. Carmichael, H. (1993) An Open Systems Approach to Quantum Optics, Springer, Berlin.
98. Goan, H.-S., Milburn, G.J., Wiseman, H. M., and Sun, H.B. (2001) Phys. Rev. B, 63, 125326.
99. Dereziński, J., De Roeck,W., and Maes, C. (2008) J. Stat. Phys., 131, 341.
100. Andrieux, D. and Gaspard, P. (2007) J. Stat. Phys., 127, 107.
101. Schaller, G., Kiesslich, G., and Brandes, T. (2010) Phys. Rev. B, 82, 041303.
102. Bulnes Cuetara, G., Esposito, M., and Gaspard, P. (2011) Phys. Rev. B, 84, 165114.
103. Cover, T.M. and Thomas, J.A. (2006) Elements of Information Theory, 2nd edn, John Wiley & Sons, Inc., Hoboken.
104. Gerritsma, E. and Gaspard, P. (2010) Biophys. Rev. Lett., 5, 163.
105. Gaspard, P. and Andrieux, D. (2011) J. Stat. Mech., P03024.
106. Cleuren, B., Van den Broeck, C., and Kawai, R. (2006) Phys. Rev. E, 74, 021117.
107. Knudsen, M. (1909) Ann. Phys., 28, 999.
108. Present, R.D. (1958) Kinetic Theory of Gases, McGraw-Hill, New York.
109. Gaspard, P. and Wang, X.-J. (1993) Phys. Rep., 235, 291.
110. Gaspard, P. (1994) Prog. Theor. Phys. Suppl., 116, 369.
111. Sánchez, R. and Büttiker, M. (2011) Phys. Rev. B, 83, 085428.
112. Sánchez, R., López, R., Sánchez, D., and Büttiker, M. (2010) Phys. Rev. Lett., 104, 076801.
113. Gillespie, D.T. (1976) J. Comput. Phys., 22, 403.
114. Golubev, D.S., Utsumi, Y., Marthaler, M., and Schön, G. (2011) Phys. Rev. B, 84, 075323.
115. Ingold, G.-L. and Nazarov, Yu.V. (1992) Single Charge Tunneling, NATO Advanced Studies Institute, Series B: Physics, Vol. 294 (eds H. Grabert and M. Devoret), Plenum, New York, pp. 21-107.
116. Förster, H. and Büttiker, M. (2008) Phys. Rev. Lett., 101, 136805.
117. Fingerle, A. (2007) C.R. Phys., 8, 696.
118. Iso, S. and Okazawa, S. (2011) Nucl. Phys. B, 851, 380.
119. Calzetta, E.A. and Hu, B.-L.B. (2008) Nonequilibrium Quantum Field Theory, Cambridge University Press, Cambridge, UK.