Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics

Physica A: Statistical Mechanics and its Applications

Volumn 369, Issue 1, 2006, Pages 201-246

  Gaspard, Pierre ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Dynamical systems; Entropy production; Escape rate; Fluctuation theorem; Hydrodynamic mode; Irreversibility; Nonequilibrium work; Time reversal symmetry; Transport coefficient

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ENTROPY; FRACTALS; NANOTECHNOLOGY; RESONANCE; STATISTICAL MECHANICS;

DYNAMICAL SYSTEMS; ESCAPE RATE; FLUCTUATION THEOREM; HYDRODYNAMIC MODE; IRREVERSIBILITY; NONEQUILIBRIUM WORK; TIME-REVERSAL SYMMETRY; TRANSPORT COEFFICIENT;

HAMILTONIANS;

EID: 33745678699     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.04.010     Document Type: Article

References (119)

1. Crommie M.F., Lutz C.P., and Eigler D.M. Science 262 (1993) 218
2. Heller E.J., Crommie M.F., Lutz C.P., and Eigler D.M. Nature 369 (1994) 464
3. DiFoggio R., and Gomer R. Phys. Rev. B 25 (1982) 3490
4. Schumack M., Linderoth T.R., Rosei F., Lægsgaard E., Stensgaard I., and Besenbacher F. Phys. Rev. Lett. 88 (2002) 156102
5. Antczak G., and Ehrlich G. Phys. Rev. Lett. 92 (2004) 166105
6. Lauhon L.J., and Ho W. Phys. Rev. Lett. 85 (2000) 4566
7. Schmidt M., Kusche R., Hippler Th., Donges J., Kronmüller W., von Issendorff B., and Haberland H. Phys. Rev. Lett. 86 (2001) 1191
8. Bustamante C., Liphardt J., and Ritort F. Phys. Today 58 (2005) 43
9. Collin D., Ritort F., Jarzynski C., Smith S.B., Tinoco Jr. I., and Bustamante C. Nature 437 (2005) 231
10. Noji H., Yasuda R., Yoshida M., and Kinosita Jr. K. Nature 386 (1997) 299
11. Yasuda R., Noji H., Yoshida M., Kinosita Jr. K., and Itoh H. Nature 410 (2001) 898
12. Fennimore A.M., Yuzvinsky T.D., Han W.-Q., Fuhrer M.S., Cumings J., and Zettl A. Nature 424 (2003) 408
13. Bourlon B., Glattli D.C., Miko C., Forró L., and Bachtold A. NanoLetters 4 (2004) 709
14. Cumings J., and Zettl A. Science 289 (2000) 602
15. Servantie J., and Gaspard P. Phys. Rev. Lett. 91 (2003) 185503
16. J. Servantie, P. Gaspard, Phys. Rev. B 73 (2006) 125428.
17. Besenbacher F., and Nørskov J.K. Science 290 (2000) 1520
18. Schmid A.K., Bartelt N.C., and Hwang R.Q. Science 290 (2000) 1561
19. Voss C., and Kruse N. Appl. Surf. Sci. 94/95 (1996) 186
20. Glansdorff P., and Prigogine I. Thermodynamics of Structure, Stability, and Fluctuations (1971), Wiley-Interscience, New York
21. Viscardy S., and Gaspard P. Phys. Rev. E 68 (2003) 041204
22. Viscardy S., and Gaspard P. Phys. Rev. E 68 (2003) 041205
23. Mareschal M., and Kestemont E. Nature 329 (1987) 427
24. Eckmann J.-P., and Ruelle D. Rev. Mod. Phys. 57 (1985) 617
25. Gaspard P., and Nicolis G. Phys. Rev. Lett. 65 (1990) 1693
26. Gaspard P., and Baras F. Phys. Rev. E 51 (1995) 5332
27. Dorfman J.R., and Gaspard P. Phys. Rev. E 51 (1995) 28
28. Gaspard P., and Dorfman J.R. Phys. Rev. E 52 (1995) 3525
29. Tél T., Vollmer J., and Breymann W. Europhys. Lett. 35 (1996) 659
30. Gaspard P. Chaos, Scattering and Statistical Mechanics (1998), Cambridge University Press, Cambridge UK
31. Dorfman J.R. An Introduction to Chaos in Nonequilibrium Statistical Mechanics (1999), Cambridge University Press, Cambridge UK
32. Evans D.J., Cohen E.G.D., and Morriss G.P. Phys. Rev. Lett. 71 (1993) 2401
33. Evans D.J., and Searles D.J. Phys. Rev. E 50 (1994) 1645
34. Gallavotti G., and Cohen E.G.D. Phys. Rev. Lett. 74 (1995) 2694
35. Kurchan J. J. Phys. A 31 (1998) 3719
36. Crooks G.E. Phys. Rev. E 60 (1999) 2721
37. Lebowitz J.L., and Spohn H. J. Stat. Phys. 95 (1999) 333
38. Maes C. J. Stat. Phys. 95 (1999) 367
39. Gaspard P. J. Chem. Phys. 120 (2004) 8898
40. Andrieux D., and Gaspard P. J. Chem. Phys. 121 (2004) 6167
41. D. Andrieux, P. Gaspard, preprint cont-mat/0512254, 2005.
42. D. Andrieux, P. Gaspard, J. Stat. Mech. (2006) P01011.
43. M. Mareschal, B.L. Holian (Eds.), Microscopic Simulations of Complex Hydrodynamic Phenomena, Plenum, New York, 1992.
44. Jarzynski C. Phys. Rev. Lett. 78 (1997) 2690
45. Evans D.J., and Searles D.J. Adv. Phys. 51 (2002) 1529
46. Gaspard P. J. Stat. Phys. 117 (2004) 599
47. Nicolis G. Introduction to Nonlinear Science (1995), Cambridge University Press, Cambridge UK
48. Krylov N.N. Nature 153 (1944) 709
49. Krylov N.N. Works on the Foundations of Statistical Mechanics (1979), Princeton University Press, Princeton, NJ
50. Ya.G. Sinai, Works on the Foundations of Statistical Mechanics, Princeton University Press, Princeton, NJ, 1979, p. 239.
51. Posch H.A., and Hoover W.G. Phys. Rev. A 38 (1988) 473
52. van Beijeren H., and Dorfman J.R. Phys. Rev. Lett. 74 (1995) 4412
53. van Beijeren H., and Dorfman J.R. Phys. Rev. Lett. 76 (1996) 3238
54. Dellago Ch., Posch H.A., and Hoover W.G. Phys. Rev. E 53 (1996) 1485
55. van Beijeren H., Dorfman J.R., Posch H.A., and Dellago Ch. Phys. Rev. E 56 (1997) 5272
56. van Zon R., van Beijeren H., and Dellago Ch. Phys. Rev. Lett. 80 (1998) 2035
57. Gaspard P., and van Beijeren H. J. Stat. Phys. 109 (2002) 671
58. Mareschal M., Kestemont E., Baras F., Clementi E., and Nicolis G. Phys. Rev. A 35 (1987) 3883
59. Gibbs J.W. Elementary Principles in Statistical Mechanics (1902), Yale University Press, New Haven reprinted by (Dover Publ. Co., New York, 1960).
60. Cornfeld I.P., Fomin S.V., and Sinai Ya.G. Ergodic Theory (1982), Springer, Berlin
61. Pollicott M. Invent. Math. 81 (1985) 413
62. Pollicott M. Invent. Math. 85 (1986) 147
63. Ruelle D. Phys. Rev. Lett. 56 (1986) 405
64. Ruelle D. J. Stat. Phys. 44 (1986) 281
65. Cvitanović P., and Eckhardt B. J. Phys. A 24 (1991) L237
66. Gaspard P., Nicolis G., Provata A., and Tasaki S. Phys. Rev. E 51 (1995) 74
67. Gaspard P., and Tasaki S. Phys. Rev. E 64 (2001) 056232
68. Tasaki S., and Gaspard P. J. Stat. Phys. 109 (2002) 803
69. Jakšić V., and Pillet C.-A. J. Math. Phys. 38 (1997) 1757
70. Jakšić V., and Pillet C.-A. J. Stat. Phys. 108 (2002) 787
71. Prosen T. Physica D 187 (2004) 244
72. P. Gaspard, in: P. Collet, et al. (Eds.), Chaotic Dynamics and Transport in Classical and Quantum Systems, Kluwer, Dordrecht, 2005, pp. 107-157.
73. Kirkwood J.G. J. Chem. Phys. 14 (1946) 180
74. Balescu R. Equilibrium and Nonequilibrium Statistical Mechanics (1975), Wiley, New York
75. W. Pauli, in: Festschrift zum 60. Geburtstage A. Sommerfelds, Hirzel, Leipzig, 1928, p. 30.
76. Nicolis G., and Prigogine I. Proc. Natl. Acad. Sci. (USA) 68 (1971) 2102
77. Nicolis G. J. Stat. Phys. 6 (1972) 195
78. Nicolis G., and Prigogine I. Self-Organization in Nonequilibrium Systems (1977), Wiley, New York
79. Nettleton R.E., and Green M.S. J. Chem. Phys. 29 (1958) 1365
80. Nicolis G., and Nicolis C. Phys. Rev. A 38 (1988) 427
81. C. Shannon, Bell System Tech. J. 27 (1948) 379, 623.
82. Kolmogorov A.N. Dokl. Akad. Nauk SSSR 124 (1959) 754
83. Sinai Ya.G. Dokl. Akad. Nauk SSSR 124 (1959) 768
84. Gaspard P., and Wang X.-J. Phys. Rep. 235 (1993) 291
85. Pesin Ya.B. Russian Math. Surv. 32 (1977) 55
86. Green M.S. J. Chem. Phys. 20 (1952) 1281
87. Green M.S. J. Chem. Phys. 22 (1954) 398
88. Kubo R. J. Phys. Soc. Japan 12 (1957) 570
89. Helfand E. Phys. Rev. 119 (1960) 1
90. Ruelle D. Thermodynamic Formalism (1978), Addison-Wesley, Reading MA
91. Kantz H., and Grassberger P. Physica D 17 (1985) 75
92. Young L.-S. Ergod. Theory Dyn. Syst. 2 (1982) 109
93. P. Gaspard, S.A. Rice, J. Chem. Phys. 90 (1989) 2225, 2242, 2255.
94. Ledrappier F., and Young L.-S. Ann. Math. 122 (1985) 509
95. van Beijeren H., Latz A., and Dorfman J.R. Phys. Rev. E 63 (2000) 016312
96. Claus I., and Gaspard P. Phys. Rev. E 63 (2001) 036227
97. Gaspard P., Claus I., Gilbert T., and Dorfman J.R. Phys. Rev. Lett. 86 (2001) 1506
98. Tasaki S., and Gaspard P. J. Stat. Phys. 81 (1995) 935
99. Gilbert T., Dorfman J.R., and Gaspard P. Nonlinearity 14 (2001) 339
100. Gaspard P. Int. J. Mod. Phys. B 15 (2001) 209
101. Gilbert T., Dorfman J.R., and Gaspard P. Phys. Rev. Lett. 85 (2000) 1606
102. Dorfman J.R., Gaspard P., and Gilbert T. Phys. Rev. E 66 (2002) 026110
103. Schnakenberg J. Rev. Mod. Phys. 48 (1976) 571
104. Luo J.-L., Van den Broeck C., and Nicolis G. Z. Phys. B-Condens. Matter 56 (1984) 165
105. Wehrl A. Rev. Mod. Phys. 50 (1978) 221
106. Brenner D.W. Phys. Rev. B 42 (1990) 9458
107. Lee S.H., and Kapral R. J. Chem. Phys. 121 (2004) 11163
108. Español P., and Zúñiga I. J. Chem. Phys. 98 (1993) 574
109. Ould-Kaddour F., and Levesque D. J. Chem. Phys. 118 (2003) 7888
110. Jülicher F., Ajdari A., and Prost J. Rev. Mod. Phys. 69 (1997) 1269
111. 1-ATPase molecular motor, preprint, 2006.
112. D. Andrieux, P. Gaspard, Fluctuation theorems and the nonequilibrium thermodynamics of molecular motors, preprint, 2006.
113. Schlögl F. Z. Phys. 248 (1971) 446
114. Schlögl F. Z. Phys. 253 (1972) 147
115. Prigogine I., and Lefever R. J. Chem. Phys. 48 (1968) 1695
116. Gillespie D.T. J. Comput. Phys. 22 (1976) 403
117. Gillespie D.T. J. Phys. Chem. 81 (1977) 2340
118. Gaspard P. J. Chem. Phys. 117 (2002) 8905
119. Claus I., and Gaspard P. Physica D 168-169 (2002) 266