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Mixing distance and stability of steady states in statistical nonlinear thermodynamics

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Zeitschrift für Physik B Condensed Matter

Abstract

The “mixing distance” introduced by E. Ruch and A. Mead defining a partial order of probability distributions is used for the discussion of the stability of steady states in nonlinear thermodynamics. A stability criterion for finite deviations is formulated, including the approach to the steady state in the sense of decreasing mixing distance as “mixing confluence”. As examples, chemically reacting systems of different types are discussed.

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References

  1. Ruch, E., Mead, A.: Theoret. Chim. Acta (Berl.)41, 95 (1976)

    Google Scholar 

  2. Ruch, E.: Theoret. Chim. Acta (Berl.)38, 167 (1975)

    Google Scholar 

  3. Shannon, C., Weaver, W.: The Mathematical Theory of Communication. Urbana: University of Illinois Press 1949

    Google Scholar 

  4. Csiszar, I.: Stud. Sci. Math. Hung.2, 299 (1967)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. Schlögl, F.: Synergetics (ed. H. Haken). Stuttgart: Teubner 1973

    Google Scholar 

  10. Schlögl, F.: Foundations of Continuum Thermodynamics (ed. J. Delgado Domingos, M.N.R. Nina, J.H. Whitelaw). London and Basingstoke: McMillan Press Ltd. 1974

    Google Scholar 

  11. Kullback, S.: Ann. Math. Statistics22, 79 (1951)

    Google Scholar 

  12. Kullback, S.: Information Theory and Statistics. New York: Wiley 1951

    Google Scholar 

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

    Google Scholar 

  14. Lasalle, J., Lefschitz, S.: Stability by Liapunov's Direct Method. New York: Acad. Press Inc. 1966

    Google Scholar 

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

    Google Scholar 

  16. Schlögl, F.: Cooperative Effects (ed. H. Haken). Amsterdam, Oxford, New York: North-Holland Publ. Comp., American Elsevier Publ. Comp. Inc.

  17. Pfaffelhuber, E.: Rough draft. Institute for Information Science, University of Tübingen 1976

  18. Glansdorff, P., Prigogine, I.: Thermodynamic Theory of Structure, Stability and Fluctuations. New York: Wiley 1971

    Google Scholar 

  19. Janssen, H.K.: Z. Physik270, 67 (1974)

    Google Scholar 

  20. Matheson, I., Walls, D.F., Gardiner, C.W.: J. Stat. Phys.12, 21 (1975)

    Google Scholar 

  21. Görtz, R.: In print

  22. Schlögl, F.: Z. Physik253, 147 (1972)

    Google Scholar 

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Schlögl, F. Mixing distance and stability of steady states in statistical nonlinear thermodynamics. Z Physik B 25, 411–421 (1976). https://doi.org/10.1007/BF01315257

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  • DOI: https://doi.org/10.1007/BF01315257

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