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Ergodicity in hard-ball systems and Boltzmann’s entropy

Zhigang Zheng, Gang Hu, and Juyuan Zhang

  • Physics Department, Beijing Normal University, Beijing 100875, China
  • Center of Theoretical Physics, China Center for Advanced Science and Technology (World laboratory), Beijing 8730, China
  • Physics Department, Siping Teacher’s College, Jilin, China

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Phys. Rev. E 53, 3246 – Published 1 April, 1996

DOI: https://doi.org/10.1103/PhysRevE.53.3246

Abstract

The ergodic property of the hard-ball systems is investigated numerically by comparing the microcanonical single-particle distributions and the corresponding numerical results in two- and three-dimensional cases. A Boltzmann-entropy-like quantity H(nc) is defined and its evolution is discussed. The deviation of this entropy from the equilibrium value obeys a power decay law in the long time limit, and the origin of this tail is explored heuristically. © 1996 The American Physical Society.

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References (27)

  1. Ya. G. Sinai, Dynamical Systems II, Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics (Spring-Verlag, Berlin, 1989).
  2. R. Jancel, Foundations of Classical and Quantum Statistical Mechanics (Pergamon, Oxford, 1969).
  3. N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, NJ, 1979).
  4. Ya. G. Sinai, Usp. Mat. Nauk 25, 141 (1970) [Russ. Math. Surv. 25, 137 (1970)].
  5. Ya. G. Sinai, N. I. Chernov, Usp. Mat. Nauk 42, 153 (1987) [Russ, Math. Surv. 42, 150 (1987)].
  6. V. L. Berdichevsky and M. V. Alberti, Phys. Rev. A 44, 858 (1991).
  7. V. L. Berdichevsky, J. Appl. Math. Mech. 52, 738 (1988).
  8. L. E. Reichl, The Transition to Chaos, In Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, Berlin, 1992).
  9. R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics, From the Pendulum to Turbulence and Chaos (Harwood, Academic, Chur, Switzerland, 1988).
  10. L. Boltzmann, Lectures on Gas Theory (Translation from German) (University of California Press, Berkeley, 1964).
  11. J. W. Gibbs, Elementary Principles in Statistical Mechanics (Dover, New York, 1902).
  12. D. Szasz, Physica A 194, 86 (1993).
  13. A. Kramli, N. Simanyi and D. Szasz, Nonlinearity 2, 311 (1989).
  14. A. Kramli, N. Simanyi and D. Szasz, Commun. Math. Phys. 129, 535 (1990).
  15. A. Kramli, N. Simanyi and D. Szasz, Ann. Math. 133, 37 (1991).
  16. A. Kramli, N. Simanyi and D. Szasz, Commun. Math. Phys. 144, 107 (1992).
  17. G. J. Ackland, Phys. Rev. E 47, 3268 (1993).
  18. Zhigang Zheng, Gang Hu, and Juyuan Zhang, Phys. Rev. E 52, 3440 (1995).
  19. L. E. Reichl, A Modern Course in Statistical Physics (University of Texas Press, Austin, 1980).
  20. B. J. Alder and T. E. Wainwright, Phys. Rev. Lett. 18, 988 (1967).
  21. M. H. Ernst, E. H. Hauge, and J. M. Van Leeuwen, Phys. Rev. A 4, 2055 (1971).
  22. S. T. Choh and G. E. Uhlenbeck, The Kinetic Theory of Dense Gases, dissertation (University of Michigan, 1958).
  23. J. R. Dorfmann and E. D. G. Cohen, Phys. Rev. A 6, 776 (1972).
  24. J. W. Dufty, Phys. Rev. A 5, 2247 (1972).
  25. H. Van Beijeren, Rev. Mod. Phys. 54, 195 (1982).
  26. F. Vivaldi, G. Casati and I. Guarneri, Phys. Rev. Lett. 51, 727 (1983).
  27. R. Brown, E. Ott and C. Grebogi, J. Stat. Phys. 49, 511 (1987).

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Phys. Rev. E 53, 3246– Published 1 April, 1996
  • Received 6 September 1995

© 1996 American Physical Society

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