Skip to main content
Log in

On the H-theorem for polyatomic gases

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The H-theorem for a classical gas of polyatomic molecules of arbitrarily complex structure is examined. A simple use of time reversal invariance of the equations of dynamics is used to circumvent the objections which were raised by Lorentz against Boltzmann's proof (nonexistence of inverse collisions).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. Boltzmann,Wien. Ber. 66:275 (1872) [also inWiss. Abh., F. Hasenöhrl, ed. (Leipzig, 1909)1:316].

    Google Scholar 

  2. C. Truesdell and R. G. Muncaster,Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Academic, New York, 1980).

    Google Scholar 

  3. H. A. Lorentz,Wien. Ber. 95:115 (1887) [also inCollected Papers, Martinus Nijhoff, ed., Vol. 6, p. 74].

    Google Scholar 

  4. S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1960).

    Google Scholar 

  5. L. Boltzmann,Vorlesungen über Gastheorie, J. A. Barth, ed. (Leipzig, 1898) Vol. 2, Chap. VII [also inLectures on Gas Theory, transl. S. G. Brush (Berkeley, 1964)].

  6. R. C. Tolman,The Principles of Statistical Mechanics (Oxford University Press, London, 1938).

    Google Scholar 

  7. G. H. Bryan,Brit. Assoc. Reports, p. 64 (1894).

  8. F. B. Pidduck,Proc. R. Soc. London Ser. A 101 (1922).

  9. L. Boltzmann,Wien Ber. 95:153 (1887) [also inWiss. Abh. 3:272].

    Google Scholar 

  10. G. E. Uhlenbeck, inThe Boltzmann Equation: Theory and Applications, E. G. D. Cohen and W. Thirring, eds.Acta Phys. Austr., Suppl. X, 107 (Springer-Verlag, Vienna, 1973).

    Google Scholar 

  11. L. Waldmann,Z. Naturforsch. 12A:660 (1957).

    Google Scholar 

  12. L. Waldmann,Z. Naturforsch. 13A:609 (1958).

    Google Scholar 

  13. R. F. Snider,J. Chem. Phys. 32:1051 (1960).

    Google Scholar 

  14. E. C. G. Stueckelberg,Helv. Phys. Acta 25:577 (1952).

    Google Scholar 

  15. L. Waldmann, inHandbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1958), Vol. 12, p. 484.

    Google Scholar 

  16. L. Waldmann, inThe Boltzmann Equation: Theory and Applications, E. G. D. Cohen and W. Thirring, eds.Acta Phys. Austr., Suppl. X, 107, (Springer-Verlag, Vienna, 1973).

    Google Scholar 

  17. C. Cercignani,Mathematical Methods in Kinetic Theory (Plenum Press, New York, and McMillan, London, 1969).

    Google Scholar 

  18. C. Cercignani,Theory and Application of the Boltzmann Equation (Scottish Academy Press, Edinburgh, and Elsevier, New York, 1975).

    Google Scholar 

  19. Y. Kagan and A. M. Afanasev,Sov. Phys. JETP 14:1096 (1962).

    Google Scholar 

  20. Y. Kagan and L. Maximov,Sov. Phys. JETP 14:604 (1962).

    Google Scholar 

  21. J. J. M. Beenakker, G. Scoles, H. F. P. Knaap, and R. M. Jonkman,Phys. Lett. 2:5 (1962).

    Google Scholar 

  22. V. D. Borman, A. S. Bruev, and L. A. Maximov,Sov. Phys. JETP 40:472 (1975).

    Google Scholar 

  23. J. J. M. Beenakker, H. F. P. Knaap, and I. Kuščer, “Correspondence between Classical and Quantum-Mechanical Boltzmann Equations”Physica,99A:265 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cercignani, C., Lampis, M. On the H-theorem for polyatomic gases. J Stat Phys 26, 795–801 (1981). https://doi.org/10.1007/BF01010940

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01010940

Key words

Navigation