Abstract
Ruch's Principle of Decreasing Mixing Distance is reviewed as a statistical physical principle and its basic suport and geometric interpretation, the Ruch-Schranner-Seligman theorem, is generalized to be applicable to a large representative class of classical statistical systems.
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References
E. Ruch and A. Schönhofer, Theorie der Chiralitätsfunktionen,Theor. Chim. Acta (Berlin)19:225–287 (1970).
E. Ruch, The diagram lattice as a structural principle,Theor. Chim. Acta (Berlin)38:167–183 (1975).
E. Ruch and I. Gutman, The branching extent of graphs,J. Combinatorics, Information Syst. Sci. 4:285–295 (1975).
E. Ruch and A. Mead, The principle of increasing mixing character and some of its consequences,Theor. Chim. Acta (Berlin)41:95–117 (1976).
E. Ruch and B. Lesche, Information extent and information distance,J. Chem. Phys. 69:393–401 (1978).
F. Schlögl, Mixing distance and stability of steady states in statistical nonlinear thermodynamics,Z. Physik B 25:411–421 (1976).
F. Schlögl and C. A. Mead, Macroscopic aspects of mixing distance in nonequilibrium thermodynamics,Ann. Phys. (N.Y.)155:172–190 (1978).
E. Ruch, The direction distance, preprint (1990).
H. Haken,Synergetics (Springer, Berlin, 1978).
E. Ruch, R. Schranner, and T. H. Seligman, Generalization of a theorem by Hardy, Littlewood, and Polya,J. Math. Anal. Appl. 76:222–229 (1980).
P. Busch and E. Ruch, The measure cone-Irreversibility as a geometrical phenomenon, Preprint (1990).
P. M. Alberti and A. Uhlmann,Math. Nachr. 97:279–295 (1980).
M. Takesaki,Theory of Operator Algebras (Springer, Berlin, 1979).
P. R. Halmos,Measure Theory (Van Nostrand, New York, 1950).
A. Dress, Populationsdynamik auf Sequenzräumen, inOrdnung aus dem Chaos, B.-O. Küppers, ed. (Piper, Munich, 1987).
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This paper is dedicated to Ernst Ruch on the occasion of his 70 th birthday.
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Busch, P., Quadt, R. On Ruch's Principle of Decreasing Mixing Distance in classical statistical physics. J Stat Phys 61, 311–328 (1990). https://doi.org/10.1007/BF01013967
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DOI: https://doi.org/10.1007/BF01013967