Can we observe microscopic chaos in the laboratory?

Advances in Chemical Physics

Volumn 99, Issue , 1997, Pages 369-392

  Gaspard, Pierre ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001454215     PISSN: 00652385     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (82)

1. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
2. Hao Bai-Lin, Ed., Chaos I & II: A Reprint Collection (World Scientific, Singapore, 1984, 1990).
3. J. Lebowitz and O. Penrose, Physics Today, February 1973, p. 23.
4. N. N. Krylov, Works on the Foundations of Statistical Mechanics (Princeton University Press, Princeton, NJ, 1979);
5. Ya. G. Sinai, Works on the Foundations of Statistical Mechanics ibid. p. 239;
6. Ya. G. Sinai and N. I. Chernov, Russ. Math. Surveys 42:3, 181 (1987).
7. P. Gaspard and G. Nicolis, Phys. Mag. (J. Belg. Phys. Soc.) 7, 151 (1985).
8. P. Gaspard, in Solitons and Chaos, I. Antoniou and F. Lambert (eds.) (Springer, Berlin, 1991), pp. 46-57.
9. R. Livi, A. Politi, and S. Ruffo, J. Phys. A: Math. Gen. 19, 2033 (1986);
10. H. A. Posch and W. G. Hoover, Phys. Rev. A 38, 473 (1988);
11. H. A. Posch and W. G. Hoover, Phys. Rev. A 39, 2175 (1989).
12. P. Gaspard and S. A. Rice, J. Chem. Phys. 90, 2225, 2242, 2255 (1989);
13. P. Gaspard and S. A. Rice, J. Chem. Phys. 91, E3279 (1989).
14. P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).
15. P. Gaspard and F. Baras, in Microscopic Simulations of Complex Hydrodynamic Phenomena, M. Maréschal and B. L. Holian (eds.) (Plenum, London, 1991), pp. 301-322;
16. P. Gaspard and F. Baras, Phys. Rev. E 51, 5332 (1995).
17. P. Cvitanović, J.-P. Eckmann, and P. Gaspard, Chaos, Solitons, and Fractals 6, 113 (1995);
18. P. Cvitanović, P. Gaspard, and T. Schreiber, Chaos 2, 85 (1992).
19. P. Gaspard, in From Phase Transitions to Chaos, G. Györgyi, I. Kondor, L. Sasvári, and T. Tél (eds.) (World Scientific, Singapore, 1992), pp. 322-334.
20. P. Gaspard, J. Stat. Phys. 68, 673 (1992).
21. P. Gaspard and D. Alonso Ramirez, Phys. Rev. A 45, 8383 (1992).
22. H. H. Hasegawa and W. C. Saphir. Phys. Lett. A 161, 471, 477 (1992);
23. H. H. Hasegawa and W. C. Saphir. Phys. Rev. A 46, 7401 (1992);
24. H. H. Hasegawa and D. J. Driebe, Phys. Lett. A 168, 18 (1992);
25. H. H. Hasegawa and D. J. Driebe, Phys. Lett. A 176, 193 (1993).
26. P. Gaspard, J. Phys. A: Math. Gen. 25 L483 (1992);
27. P. Gaspard, Phys. Lett. A 168, 13 (1992).
28. S. Tasaki, I. Antoniou, and Z. Suchanecki, Phys. Lett. A 179, 97 (1993);
29. I. Antoniou and S. Tasaki, J. Phys. A: Math. Gen. 26, 73 (1993);
30. I. Antoniou and S. Tasaki, Physica A 190, 303 (1992).
31. P. Gaspard, Chaos 3, 427 (1993);
32. Phys. Rev. E 53, 4379 (1996).
33. S. A. Rice, P. Gaspard, and K. Nakamura, Adv. Class. Traj. Meth. 1, 215 (1991).
34. P. Cvitanović and B. Eckhardt, J. Phys. A: Math. Gen. 24, L237 (1991).
35. P. Gaspard, in Quantum Chaos, G. Casati, I. Guarneri, and U. Smilansky (eds.) (North-Holland, Amsterdam, 1993), pp. 307-383.
36. I. Prigogine, Nonequilibrium Statistical Mechanics (Wiley, New York, 1962);
37. I. Prigogine, From Being to Becoming (Freeman, San Francisco, 1980).
38. K. F. Gauss, J. Reine Angew. Math. IV, 232 (1829).
39. S. Smale, in The Mathematics of Time (Springer, New York, 1980), p. 137.
40. S. Nosé, J. Chem. Phys. 81, 511 (1984);
41. Mol. Phys. 52 255 (1984);
42. W. G. Hoover, Phys. Rev. A 31, 1695 (1985).
43. D. J. Evans, E. G. D. Cohen, and M. P. Morris, Phys. Rev. A 42, 5990 (1990).
44. N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Ya. G. Sinai, Phys. Rev. Lett. 70, 2209 (1993).
45. S. Tasaki and P. Gaspard, in Toward the Harnessing of the Chaos, M. Yamaguti (ed.) (Elsevier Science B. V., 1994), pp. 273-288;
46. J. Stat. Phys. 81, 935 (1995).
47. M. Hara and M. Yamaguti, Jpn. J. Appl. Math. 1, 183 (1984).
48. P. Gaspard and X.-J. Wang, Phys. Rep. 235, 321 (1993).
49. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, Urbana, 1949).
50. A. N. Kolmogorov, Dokl. Acad. Sci. USSR 124:4, 754 (1959);
51. Ya. G. Sinai, Dokl. Acad. Sci. USSR ibid. 124:4, 768 (1959).
52. G. J. Chaitin, Algorithmic Information Theory (Cambridge University Press, Cambridge, 1987).
53. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968);
54. P. Billingsley, Ergodic Theory and Information (Wiley, New York, 1965);
55. I. P. Comfeld, S. V. Fomin, and Ya. G. Sinai, Ergodic Theory (Springer, Berlin, 1982).
56. M. S. Green, J. Chem. Phys. 22, 398 (1954);
57. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
58. Ya. B. Pesin, Math. USSR Izv. 10(6), 1261 (1976);
59. Russ. Math. Surveys 32(4), 55 (1977).
60. H. Kantz and P. Grassberger, Physica D 17, 75 (1985).
61. P. Szépfalusy and T. Tél, Phys. Rev. A 34, 2520 (1986);
62. P. Szépfalusy and T. Tél, Phys. Rev. A 35, 477 (1987).
63. D. Ruelle, Ann. NY Acad. Sci. 316, 408 (1979);
64. Ju. I. Kifer, Math. SSSR Izv. 8, 1083 (1974).
65. A. N. Kolmogorov, IRE Trans. Inf. Theory 1, 102 (1956);
66. A. N. Kolmogorov and V. M. Tikhomirov, Uspekhi Mat. Nauk 14, 3 (1959);
67. V. M. Tikhomirov, Russ. Math. Surveys 18, 51 (1963).
68. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968).
69. A. Cohen and I. Procaccia, Phys. Rev. A 31, 1872 (1985).
70. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981), p. 358 and references therein.
71. P. Résibois and M. De Leener, Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
72. J. L. Lebowitz and E. Rubin, Phys. Rev. 131, 2381 (1963);
73. P. Résibois and H. T. Davis, Physica 30, 1077 (1964).
74. L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1963).
75. J. Perrin, Les atomes (Presses Universitaires de France, Paris, 1970).
76. G. Nicolis and P. Gaspard, Chaos, Solitons, and Fractals 4, 41 (1994).
77. P. Gaspard, in Quantum Chaos - Quantum Measurement, P. Cvitanović, I. Percival, and A. Wirzba (eds.) (Kluwer, The Netherlands, 1992), pp. 19-42.
78. P. Gaspard, in Quantum Chaos, H. A. Cerdeira, M. C. Gutzwiller, R. Ramaswamy, and G. Casati (eds.) (World Scientific, Singapore, 1991), p. 348;
79. T. Hudetz and P. Gaspard, unpublished.
80. P. Gaspard, Prog. Theor. Phys. Suppl. 116, 369 (1994).
81. J. R. Dorfman and P. Gaspard, Phys. Rev. E 51, 28 (1995);
82. P. Gaspard and J. R. Dorfman, Phys. Rev. E 52, 3525 (1995).