Skip to main content
SpringerLink
Log in

H-theorem for a linear kinetic theory

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

Abstract

A strongH-theorem is proved for the approximate linear kinetic theory of Bławzdziewicz and Cichocki, obtained by truncating a transformed hierarchy of evolution equations. For an ith truncation we define an entropy functional that is strictly increasing in time, unless the ith reduced distribution function depends on position coordinates only. It also follows that the only stationary solution of the linear kinetic theory is the equilibrium solution. In addition, we show that the usual symmetry properties of equilibrium time correlation functions are preserved by the approximate kinetic theory under consideration.

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. Karkheck and G. Stell,Phys. Rev. A 25:3302 (1982).

    Google Scholar 

  2. J. Karkheck, H. van Beijeren, I. de Schepper, and G. Stell,Phys. Rev. A 32:2517 (1985).

    Google Scholar 

  3. J. Bławzdziewicz and G. Stell,J. Stat. Phys. 56:821 (1989).

    Google Scholar 

  4. H. van Beijeren, inFundamental Problems in Statistical Mechanics, Vol. VII, H. van Beijeren, ed. (North-Holland, Amsterdam, 1990).

    Google Scholar 

  5. P. Résibois,Physica A 94:1 (1978).

    Google Scholar 

  6. P. Résibois,J. Stat. Phys. 19:593 (1978).

    Google Scholar 

  7. J. Bławzdziewicz and B. Cichocki,Physica A 127:38 (1984); referred to as I. 8. B. Cichocki,Physica A 142:245 (1987); referred to as II.

    Google Scholar 

  8. M. H. Ernst, J. R. Dorfman, W. R. Hogey, and J. M. J. van Leeuwen,Physica 45:127 (1969).

    Google Scholar 

  9. J. Piasecki, inFundamental Problems in Statistical Mechanics, Vol. IV, E. G. D. Cohen and W. Fiszdon, eds. (Ossolineum, Wrocław, 1978).

    Google Scholar 

  10. H. van Beijeren, Kinetic theory of hard spheres, Ph. D. thesis, University of Nijmegen (1974); H. van Beijeren and M. H. Ernst,J. Stat. Phys. 21:125 (1979).

  11. J. Bławzdziewicz, B. Cichocki, and R. Hołyst,Physica A 157:857 (1989); R. Hołyst, J. Bławzdziewicz, and B. Cichocki, unpublished.

    Google Scholar 

  12. E. G. D. Cohen and I. M. de Schepper,J. Stat. Phys. 46:949 (1987).

    Google Scholar 

  13. G. Szamel,J. Stat. Phys. 55:381 (1989).

    Google Scholar 

  14. J. A. Leegwater, H. van Beijeren, and J. Michels,J. Phys. Condensed Matter 1:237 (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Utrecht, 3508, TA Utrecht, The Netherlands

    J. Bklawzdziewicz & H. van Beijeren

  2. Institute of Theoretical Physics, Warsaw University, 00681, Hoża 69, Warsaw, Poland

    B. Cichocki

  3. Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049, Warsaw, Poland

    B. Cichocki

Authors
  1. J. Bklawzdziewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Cichocki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. van Beijeren
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

On leave of absence from Institute of Physics, Szczecin University, Wielkopolska 15, Szczecin, Poland.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bklawzdziewicz, J., Cichocki, B. & van Beijeren, H. H-theorem for a linear kinetic theory. J Stat Phys 66, 607–633 (1992). https://doi.org/10.1007/BF01060084

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060084

Key words

Search

Navigation