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.
Similar content being viewed by others
References
Ruch, E., Mead, A.: Theoret. Chim. Acta (Berl.)41, 95 (1976)
Ruch, E.: Theoret. Chim. Acta (Berl.)38, 167 (1975)
Shannon, C., Weaver, W.: The Mathematical Theory of Communication. Urbana: University of Illinois Press 1949
Csiszar, I.: Stud. Sci. Math. Hung.2, 299 (1967)
Schlögl, F.: Z. Physik191, 81 (1966)
Schlögl, F.: Z. Physik198, 559 (1967)
Schlögl, F.: Z. Physik243, 303 (1971)
Schlögl, F.: Z. Physik248, 446 (1971)
Schlögl, F.: Synergetics (ed. H. Haken). Stuttgart: Teubner 1973
Schlögl, F.: Foundations of Continuum Thermodynamics (ed. J. Delgado Domingos, M.N.R. Nina, J.H. Whitelaw). London and Basingstoke: McMillan Press Ltd. 1974
Kullback, S.: Ann. Math. Statistics22, 79 (1951)
Kullback, S.: Information Theory and Statistics. New York: Wiley 1951
Rényi, A.: Wahrscheinlichkeitsrechnung. Berlin: VEB Deutscher Verlag der Wissenschaften 1966
Lasalle, J., Lefschitz, S.: Stability by Liapunov's Direct Method. New York: Acad. Press Inc. 1966
Schlögl, F.: Z. Physik249, 1 (1971)
Schlögl, F.: Cooperative Effects (ed. H. Haken). Amsterdam, Oxford, New York: North-Holland Publ. Comp., American Elsevier Publ. Comp. Inc.
Pfaffelhuber, E.: Rough draft. Institute for Information Science, University of Tübingen 1976
Glansdorff, P., Prigogine, I.: Thermodynamic Theory of Structure, Stability and Fluctuations. New York: Wiley 1971
Janssen, H.K.: Z. Physik270, 67 (1974)
Matheson, I., Walls, D.F., Gardiner, C.W.: J. Stat. Phys.12, 21 (1975)
Görtz, R.: In print
Schlögl, F.: Z. Physik253, 147 (1972)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01315257