Skip to main content
SpringerLink
Log in

A characteristic class of quantities in nonequilibrium thermodynamics and a statistical justification of the local equilibrium approximation

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

Starting from entropy in equilibrium thermodynamics, defined as the mean value of a bit-number, the cumulants of this bit-number are discussed. Moreover, relative bit-numbers of two probability distributions, and their cumulants are considered. All these cumulants are additive quantities for independent systems, and are invariants with respect to reversible motion. The cumulants of lowest order are well known quantities in statistical thermodynamics, which play important roles in nonequilibrium thermodynamics as well. Their reversibility invariance gives a justification of the macroscopic approximation by “local equilibrium” for hydrodynamic system on a very general level.

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. Shannon, C., Weaver, W.: The mathematical theory of communication. Urbana: University of Illinois Press 1949

    Google Scholar 

  2. Kubo, R.: J. Phys. Soc. Japan17, 1100 (1962)

    Google Scholar 

  3. Schlögl, F.: Z. Physik249, 1 (1971)

    Google Scholar 

  4. Kullback, S.: Information theory and statistics. New York: Wiley 1951

    Google Scholar 

  5. Rényi, A.: Wahrscheinlichkeitsrechnung. Berlin: VEB Deutscher Verlag der Wissenschaften 1966

    Google Scholar 

  6. Schlögl, F.: Z. Physik191, 81 (1966)

    Google Scholar 

  7. Schlögl, F.: Z. Physik198, 559 (1967)

    Google Scholar 

  8. Schlögl, F.: Z. Physik243, 303 (1971)

    Google Scholar 

  9. Schlögl, F.: Z. Physik248, 446 (1971)

    Google Scholar 

  10. Schlögl, F.: Phys. Letters36 A, 193 (1971)

    Google Scholar 

  11. Glansdorff, P., Prigogine, I.: Physica46, 344 (1970)

    Google Scholar 

  12. Glansdorff, P., Prigogine, I.: Thermodynamic theory of structure, stability and fluctuations. New York: Wiley 1971

    Google Scholar 

  13. Schlögl, F.: Z. Physik267, 77 (1974)

    Google Scholar 

  14. Mori, H.: J. Phys. Soc. Japan11, 1029 (1956)

    Google Scholar 

  15. Mc Lennan, J.A.: In: Advances in chemical physics, ed. I. Prigogine. New York: Interscience Publishers, Inc. 1963

    Google Scholar 

  16. Zubarev, D.N.: Soviet Phys. Doklady10, 526 (1965)

    Google Scholar 

  17. Bausch, R.: Z. Physik244, 190 (1971)

    Google Scholar 

  18. Janssen, H.K.: Z. Physik253, 176 (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Rheinisch-Westfälischen Techn. Hochschule, D-5100, Aachen, Templergraben, Federal Republic of Germany

    F. Schlögl

Authors
  1. F. Schlögl
    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

Schlögl, F. A characteristic class of quantities in nonequilibrium thermodynamics and a statistical justification of the local equilibrium approximation. Z Physik B 20, 177–184 (1975). https://doi.org/10.1007/PL00020762

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/PL00020762

Keywords

Search

Navigation