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Approximate kinetic theory of hard-sphere fluids near equilibrium. I. Formal theory

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Abstract

We propose a kinetic theory of hard-sphere fluids which systematically generalizes the Enskog equation by taking successively into account binary, ternary,... dynamic correlations in a system close to equilibrium. The first approximation, beyond Enskog, is displayed explicitly; it reproduces most of the results previously established in limiting cases (short-and long-time behavior, low-density expansions) and appears to give a good description of hard-sphere dynamics for all times and all densities. This explicit study will be presented in another publication.

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References

  1. R. Zwanzig,Phys. Chem. 16:67 (1965).

    Google Scholar 

  2. J. Lebowitz and J. Percus,Phys. Rev. 155:122 (1967).

    Google Scholar 

  3. (a)N. Ailawadi, A. Rahman, and R. Zwanzig,Phys. Rev. A 4:1616 (1972);

    Google Scholar 

  4. J. Lebowitz, J. Percus, and J. Sykes,Phys. Rev. 188:487 (1969)

    Google Scholar 

  5. G. Mazenko,Phys. Rev.A 7:209, 222 (1973).

    Google Scholar 

  6. B. Alder, D. Gass, and T. Wainwright,J. Chem. Phys. 53:3813 (1970).

    Google Scholar 

  7. A. Rahman,Phys. Rev. 136A:405 (1964).

    Google Scholar 

  8. D. Levesque and L. Verlet,Phys. Rev. A 2:2514 (1970).

    Google Scholar 

  9. J. Kushick and B. Berne,J. Chem. Phys. 59:3732 (1973); D. Levesque, to be published.

  10. J. Piasecki and P. Resibois,J. Math. Phys. 14:1984 (1973); P. Resibois, Y. Pomeau, and J. Piasecki,J. Math. Phys. 15:1238 (1974).

    Google Scholar 

  11. P. Resibois, C. Joukoff, and M. Theosodopolu, to be published.

  12. O. Landford, Time evolution of large classical systems, in Proc. Battelle Rencontres on Dynamical Systems, Springer-Verlag, Berlin (1975).

    Google Scholar 

  13. S. Choh and G. Uhlenbeck. The kinetic theory of phenomena in dense gases, University of Michigan, 1958 (unpublished).

  14. J. Sengers, Acta Physica Austriaca,Suppl. V 1973:177–308.

    Google Scholar 

  15. J. Dorfman and E. Cohen,Phys. Lett. 16:124 (1963); K. Kawasaki and I. Oppenheim, Phys. Rev. 136A:1519 (1964).

    Google Scholar 

  16. Y. Pomeau and P. Resibois, Physics Reports (to appear), and references quoted therein.

  17. J. Dorfman and E. Cohen,Phys. Rev. Lett. 23:1257 (1960); Phys. Rev. A 6:776 (1972).

    Google Scholar 

  18. P. Resibois, to be published.

  19. G. Gross,Ann. Phys. (N. Y.) 69:42 (1972);J. Stat. Phys. 9:275, 297 (1973); K. D. Bergeron, E. P. Gross, and R. L. Varley,J. Stat. Phys. 10:111 (1974).

    Google Scholar 

  20. D. Massignon,Mécanique Statistique des Fluides, Dunod, Paris (1957).

    Google Scholar 

  21. M. Ernst, J. Dorfman, W. Hoegy, and J. Van Leeuwen,Physica 45:127 (1969).

    Google Scholar 

  22. I. Prigogine,Non-Equilibrium Statistical Mechanics, Interscience, New York (1962).

    Google Scholar 

  23. P. Resibois,J. Stat. Phys. 2:21 (1970).

    Google Scholar 

  24. R. Zwanzig,Phys. Rev. 129:486 (1963).

    Google Scholar 

  25. J. Sengers, M. Ernst, and D. Gillespie,J. Chem. Phys. 56:5583 (1972).

    Google Scholar 

  26. G. Gallavotti, O. Lanford, and J. Lebowitz,J. Math. Phys. 11:2898 (1970).

    Google Scholar 

  27. S. Goldstein, J. L. Lebowitz, and M. Aizenman, Ergodic properties of infinite systems, in Proc. Battelle Rencontres on Dynamical Systems, Springer-Verlag Berlin (1975).

    Google Scholar 

  28. Y. Sinai, in Statistical Mechanics, Foundations and Applications, T. A. Bak, ed., Benjamin, New York (1967);Usp. Mat. Nauk 27:137 (1972); L. Bunimovich and Y. Sinai,Mat. Sb. 90:416 (1973).

    Google Scholar 

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Supported by U. S. AFOSR Grant 73-2430B.

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Resibois, P., Lebowitz, J.L. Approximate kinetic theory of hard-sphere fluids near equilibrium. I. Formal theory. J Stat Phys 12, 483–516 (1975). https://doi.org/10.1007/BF01025835

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