Journal of Statistical Physics

, Volume 32, Issue 1, pp 71–80 | Cite as

The entropy of the BKW solution

  • Christian J. Tourenne
Articles

Abstract

The entropy of thed-dimensional generalization of the BKW solution of the homogeneous Boltzmann equation is calculated and expressed ford = 3 in terms of error functions. It is verified that the McKean conjecture cannot hold in most of the time domain where thed-dimensional BKW solution is defined.

Key words

Boltzmann entropy BKW solution hypergeometric function McKean conjecture 

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References

  1. 1.
    A. V. Bobylev,Sov. Phys. Dokl. 20:820 (1976).Google Scholar
  2. 2.
    M. Krook and T. T. Wu,Phys. Rev. Lett. 36:1107 (1976).Google Scholar
  3. 3.
    M. H. Ernst, inFundamental Problems in Statistical Mechanics V, E.G.D. Cohen, ed. (North Holland, Amsterdam, 1980).Google Scholar
  4. 4.
    M. H. Ernst,Phys. Lett. 69A:390 (1979).Google Scholar
  5. 5.
    R. M. Ziff,Phys. Rev. A 23:916 (1981).Google Scholar
  6. 6.
    H. P. McKean,Arch. Ration. Mech. Anal. 21:343 (1966).Google Scholar
  7. 7.
    S. Harris,J. Math. Phys. 8:2407 (1967).Google Scholar
  8. 8.
    S. Harris,J. Chem. Phys. 48:4012 (1968).Google Scholar
  9. 9.
    S. Simons,J. Phys. A2:12 (1969).Google Scholar
  10. 10.
    S. Simons,Phys. Lett. 33A:154 (1970).Google Scholar
  11. 11.
    S. Simons,J. Phys. A5:1537 (1972).Google Scholar
  12. 11.
    S. Rouse and S. Simons,J. Phys.,A11:423 (1978).Google Scholar
  13. 13.
    R. M. Ziff, S. D. Merajver, and G. Stell,Phys. Rev. Lett. 47:1493 (1981).Google Scholar
  14. 14.
    G. Garret,J. Phys. A15:L351 (1982).Google Scholar
  15. 15.
    E. H. Lieb,Phys. Rev. Lett. 48:1057 (1982).Google Scholar
  16. 16.
    K. Olaussen,Phys. Rev. A 25:3393 (1982).Google Scholar
  17. 17.
    D. Sherrington and S. Kirkpatrick,Phys. Rev. Lett. 35:1792 (1975).Google Scholar
  18. 18.
    V. J. Emery,Phys. Rev. B 11:239 (1975).Google Scholar
  19. 19.
    M. Abramowitz and I. Stegun,Handbook of Mathematical Formulas (US Government Printing Office, Washington, D.C., 1965).Google Scholar
  20. 20.
    E. T. Whittaker and G. N. Watson,A Course of Modern Analysis (Cambridge University Press, Cambridge, 1963).Google Scholar
  21. 21.
    J. Tjon and T. T. Wu,Phys. Rev. A 19:883 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Christian J. Tourenne
    • 1
  1. 1.Physics DepartmentMaharishi International UniversityFairfield

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