Statistical Inequalities and Thermodynamics of Open Systems

  • F. Schlögl
Chapter

Abstract

A relative measure K for a probability distribution p with respect to a reference distribution p’ turns out to be very useful in statistical thermodynamics of open systems. p’ can describe the influence of the environment. With this notion the stability conditions of thermostatics are obtained directly. The Glansdorff—Prigogine stability criterion for steady nonequilibrium states, with the inclusion of final perturbations and Meixner’s passivity conditions, can be deduced in statistical theory. K is connected with the probability of fluctuations in a stable steady state. That gives rise to relations between dynamics of small fluctuations and their correlations. With an adequate measure K for density matrices essentially all the results can be achieved by quantum theory. Heat capacity is related to another general statistical measure for probability distributions, and can be generalised to nonequilibrium states, especially to nonequilibrium phase transitions.

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References

  1. 1.
    J. Rayski. Refined interpretation of quantum mechanics. Talk on Symposium on Mathematical Physics, University Torun, Poland, December 1972Google Scholar
  2. 2.
    C. Shannon and W. Weaver. The mathematica! theorie of communication, Urbana, Univ. of Illinois Press (1949)Google Scholar
  3. 3.
    S. Kullback. Annals of Math. Statistics, 22 (1951), 79CrossRefGoogle Scholar
  4. 4.
    S. Kullback. Information Theory and Statistics, Wiley, New York (1951)Google Scholar
  5. 5.
    A. Rényi. Wahrscheinlichkeitsrechnung, VEB Deutscher Verlag der Wissenschaften, Berlin (1966)Google Scholar
  6. 6.
    A. Hobson and B. K. Cheng. Journal of Statistical Physics, 7 (1973), 301CrossRefGoogle Scholar
  7. 7.
    E. T. Jaynes. Phys. Rev., 106 (1957), 620CrossRefGoogle Scholar
  8. 8.
    F. Schlögl. Z. Physik, 191 (1966), 81CrossRefGoogle Scholar
  9. 9.
    F. Schlögl. Z. Physik, 198 (1967), 559CrossRefGoogle Scholar
  10. 10.
    S. R. de Groot. Thermodynamics of Irreversible Processes, North-Holland Publ. Co., Amsterdam (1951)Google Scholar
  11. 11.
    J. Meixner and H. G. Reik. Handbuch der Physik, III, 2, Springer, Berlin-GöttingenHeidelberg (1959)Google Scholar
  12. 12.
    H. Mori. Phys. Rev., 115 (1959), 298CrossRefGoogle Scholar
  13. 13.
    P. Glansdorff and I. Prigogine. Structure, Stabilité et Fluctuations, Masson, Paris (1971)Google Scholar
  14. 14.
    F. Schlögl. Z. Physik, 253 (1972), 147CrossRefGoogle Scholar
  15. 15.
    R. Graham and H. Haken. Z. Physik, 237 (1970), 31CrossRefGoogle Scholar
  16. 16.
    H. Haken. In Festkörperprobleme X, ed. by O. Madelung, Braunschweig, Vieweg (1970)Google Scholar
  17. 17.
    V. de Giorgio and M. O. Scully. Phys. Rev., A2 (1970), 1170CrossRefGoogle Scholar
  18. 18.
    S. Grossmann and P. H. Richter. Z. Physik, 242 (1971), 458CrossRefGoogle Scholar
  19. 19.
    V. Dohm. Solid State Commun., 11 (1972), 1273CrossRefGoogle Scholar
  20. 20.
    V. Dohm. Dissertation, Aachen (1973)Google Scholar
  21. 21.
    E. Pytte and H. Thomas. Phys. Rev., 179 (1969), 431CrossRefGoogle Scholar
  22. 22.
    J. W. F. Woo and Landauer. I.E.E.E. J. Qu. El., 7 (1971), 435Google Scholar
  23. 23.
    R. Landauer and J. W. F. Woo. IBM Research (1972)Google Scholar
  24. 24.
    P. Glansdorff and I. Prigogine. Physica, 46 (1970), 344CrossRefGoogle Scholar
  25. 25.
    F. Schlögl. Z. Physik, 248 (1971), 446CrossRefGoogle Scholar
  26. 26.
    H. K. Janssen. Z. Physik, 253 (1972), 176CrossRefGoogle Scholar
  27. 27.
    J. A. McLennan. Advances in Chemical Physics, ed. by J. Prigogine, Interscience, New York (1963)Google Scholar
  28. 28.
    D. N. Zubarev. Soviet Phys. Doklady, 10 (1965), 526Google Scholar
  29. 29.
    R. Bausch. Z. Physik, 244 (1971), 190CrossRefGoogle Scholar
  30. 30.
    I. Prigogine. Étude Thermodynamique des Phénomènes Irreversibles, Desoer, Liege (1947)Google Scholar
  31. 31.
    P. Mazur. Bull. Acad. Roy. Belgique Cl. Sc., 38 (1952), 182Google Scholar
  32. 32.
    J. Meixner. ARPA-SD 86 Report E25, Division of Engineering, Brown University, Providence, R. I. (1965)Google Scholar
  33. 33.
    J. Meixner. Z. Physik, 219 (1969), 79CrossRefGoogle Scholar
  34. 34.
    J. Meixner. Arch. Rat. Mech. Anal., 33 (1969), 33CrossRefGoogle Scholar
  35. 35.
    F. Schlögl, Z. Physik, 244 (1971), 199CrossRefGoogle Scholar
  36. 36.
    R. F. Greene and H. B. Callen. Phys. Rev., 83 (1951), 1231CrossRefGoogle Scholar
  37. 37.
    F. Schlögl. Physics Letters, 36A (1971), 193CrossRefGoogle Scholar
  38. 38.
    F. Schlögl. Z. Physik, 249 (1971), 1CrossRefGoogle Scholar

Copyright information

© Instituto de Alta Cultura-Núcleo de Estudos de Engenharia Mecanica 1973

Authors and Affiliations

  • F. Schlögl
    • 1
  1. 1.Institut für Theoretische PhysikRWTH AachenAachenGermany

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