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The problem of equivalence in statistical mechanics of equilibrium

✍ Scribed by J. Schröter; R. Wegener

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
432 KB
Volume
14
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The physical problem of the equivalence of certain partition function in statistical mechanics leads to the following mathematical problem: Under what conditions is the logarithm of a Laplace–Stieltjes transform of the so‐called microcanonical partition function equal to a Legendre transform of the logarithm of the latter? The conditions we shall formulate turn out to be physically reasonable.

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and for n # N, let 8(n) be the number of matrices C which are products of A's and B's where both A and B must occur, such that the trace tr(C)=n. It has been conjectured that This conjecture is disproved by showing that , has an absolutely continuous limit distribution with respect to the Lebesque