Skip to main content
SpringerLink
Log in

Kinetic equation approach to phase transitions

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

Abstract

An exact mathematical discussion of the linearized Enskog-Vlasov equation is given. A criterion for the occurrence of the linear instability is related to a criterion for the occurrence of the bifurcation of the equilibrium stationary solution to the nonlinear Enskog-Vlasov equation. Mathematical results are interpreted physically in connection with phase transitions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. G. Kirkwood and E. Monroe,J. Chem. Phys. 9:514 (1941); J. G. Kirkwood, inPhase Transformation in Solids (R. Smoluchowski, J. E. Meyer, and W. A. Weyl, ed.), John Wiley and Sons, New York, 1951.

    Google Scholar 

  2. D. Ruelle,Statistical Mechanics (Rigorous Results), W. A. Benjamin, New York, 1969, 5.7.

    Google Scholar 

  3. L. A. Segel, inNonequilibrium Thermodynamics, Variational Techniques and Stability (R. J. Donnelley, R. Herman, and I. Prigogine, eds.), University of Chicago Press, Chicago, 1966.

    Google Scholar 

  4. I. Prigogine and G. Nicolis,J. Chem. Phys. 45:3342 (1967); I. Prigogine and L. Lefever,J. Chem. Phys. 48:1695 (1968).

    Google Scholar 

  5. P. Glansdorff and I. Prigogine,Physica 45:344 (1970).

    Google Scholar 

  6. E. Hopf,Commun. Pure Appl. Math. 1:303 (1948).

    Google Scholar 

  7. L. de Sobrino,Can. J. Phys. 45:363 (1967).

    Google Scholar 

  8. K. Kawasaki,Progr. Theoret. Phys. 41:1190 (1969).

    Google Scholar 

  9. N. D. Mermin,Ann. Phys. (N.Y.) 18:421, 454 (1962).

    Google Scholar 

  10. R. L. Liboff,Phys. Rev. 131:2318 (1963).

    Google Scholar 

  11. D. Wisnivesky,Phys. Fluids 12:447 (1969).

    Google Scholar 

  12. H. Grad,Phys. Fluids 6:147 (1963).

    Google Scholar 

  13. G. Sandri, A. Kritz, and F. Schatzmann,Ann. Phys. (N.Y.) 43:452 (1967).

    Google Scholar 

  14. M. Grmela and J. Kyncl,Can. J. Phys. 47:2815 (1969); M. Grmela and J. Votruba,Can. J. Phys. 47:2283 (1969).

    Google Scholar 

  15. M. Nelkin and A. Ghatak,Phys. Rev. 135:A4 (1964).

    Google Scholar 

  16. J. L. Lebowitz, J. K. Percus, and J. Sykes,Phys. Rev. 188:487 (1969).

    Google Scholar 

  17. F. Hofelich,Z. Physik 226:395 (1969).

    Google Scholar 

  18. M. Grmela,Kernenergie 11:33 (1968).

    Google Scholar 

  19. O. Penrose,Phys. Fluids 3:258 (1960).

    Google Scholar 

  20. E. P. Gross and D. Wisnivesky,Phys. fluids 11:1387 (1968).

    Google Scholar 

  21. D. Wisnivesky,Phys. Fluids 12:724 (1969).

    Google Scholar 

  22. N. G. van Kampen,Phys. Rev. 135:A362 (1964).

    Google Scholar 

  23. J. L. Lebowitz and O. Penrose,J. Math. Phys. 7:98 (1966).

    Google Scholar 

  24. D. J. Gates and O. Penrose,Commun. Math. Phys. 17:194 (1970).

    Google Scholar 

  25. L. H. Dymond and B. J. Alder,J. Chem. Phys. 45:2061 (1967);48:343 (1968);52:923 (1970).

    Google Scholar 

  26. W. B. Strickfaden and L. de Sobrino,Can. J. Phys. 48:2507 (1970).

    Google Scholar 

  27. K. K. Kobayashi,J. Phys. Soc. Japan 27:1116 (1969).

    Google Scholar 

  28. R. Bellmann, G. Birkhoff, and I. Abu-Shumays (eds.),Transport Theory, American Mathematical Society, Providence, Rhode Island, 1969.

    Google Scholar 

  29. P. Gray, inPhysics of Simple Liquids (H. N. V. Temperlay, J. Rowlinson, and G. S. Rushbrook, eds.), North-Holland Publ. Co., Amsterdam, 1968.

    Google Scholar 

  30. E. G. D. Cohen, inLectures in Theoretical Physics IXC (W. E. Brittin, ed.), Boulder, Gordon and Breach, New York, 1967, p. 279.

    Google Scholar 

  31. L. D. Landau,Soviet Phys. 11:26 (1937).

    Google Scholar 

  32. A. A. Vlasov,Many Particle Theory and Its Application to Plasma, Gordon and Breach, New York, 1961;Statistical Distribution Functions (in Russian), Moscow, 1966.

    Google Scholar 

  33. W. B. Strickfaden, Thesis, University of British Columbia (1970), and paper in preparation.

  34. J. D. Weeks, S. A. Rice, and J. J. Kozak,J. Chem. Phys. 52:2415 (1970) (and references cited therein).

    Google Scholar 

  35. V. I. Zubov and Y. P. Terletsky,Ann. Physik 24:97 (1970).

    Google Scholar 

  36. H. N. V. Temperley, inStatistical Mechanics, Foundations and Applications, (T. A. Bak, ed.), W. A. Benjamin, New York, 1967, p. 368.

    Google Scholar 

  37. M. S. Green,J. Math. Phys. 9:875 (1968).

    Google Scholar 

  38. J. B. Keller and S. Antman (Eds.),Bifurcation Theory and Nonlinear Eigenvalue Problems, W. A. Benjamin, New York, 1969.

    Google Scholar 

  39. C. Cercignani,Mathematical Methods in Kinetic Theory, Plenum Press, New York, 1969.

    Google Scholar 

  40. S. Ranganathan and M. Nelkin,J. Chem. Phys. 47:4068 (1967).

    Google Scholar 

  41. T. Kato,Perturbation Theory for Linear Operators, Springer Verlag, New York, 1966.

    Google Scholar 

  42. L. Sirovich and J. K. Thurber,J. Math. Phys. 10:239 (1969).

    Google Scholar 

  43. H. Grad, inRarefied Gas Dynamics (J. A. Laurmann, ed.), Academic Press, New York, 1963.

    Google Scholar 

  44. A. C. Zaanen,Linear Analysis, North-Holland Publ. Co., Amsterdam, 1960, p. 317.

    Google Scholar 

  45. B. J. Matkowsky,SIAM J. Appl. Math. 18:872 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of British Columbia, Vancouver, Canada

    M. Grmela

Authors
  1. M. Grmela
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grmela, M. Kinetic equation approach to phase transitions. J Stat Phys 3, 347–364 (1971). https://doi.org/10.1007/BF01011389

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01011389

Key words

Search

Navigation