Communications in Mathematical Physics - Volume 225 - download pdf or read online

By M. Aizenman (Chief Editor)

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Phys. 61, no. 1/2, 387–402 (1990) 9. : Dynamical systems of statistical mechanics. In: Dynamical Systems, Ergodic Theory and Applications, Encyclopaedia of Mathematical Sciences, V. 100. Berlin: Springer, 2000, pp. 384–431 10. : On the problem of the mathematical foundation of the Gibbs postulate in classical statistical mechanics. In: Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, V. 80. Berlin: Springer-Verlag 1978, pp. 325–340 11. : On convergence to equilibrium distribution.

175, 231–266 (1987) 33. : Stationary non equilibrium states of infinite harmonic systems. Commun. Math. Phys. 54, 97–120 (1977) 34. : Thermodynamics and Statistical Mechanics. New York: Academic Press, 1956 35. : Behaviour for large time of solutions of the Klein–Gordon equation. Trans. Moscow Math. Soc. 30, 139–158 (1976) 36. R.. Asymptotic Methods in Equations of Mathematical Physics. New York–London–Paris: Gordon and Breach, 1989 37. : Mathematical Problems of Statistical Hydromechanics. Dordrecht; Kluwer Academic Publishers, 1988 Communicated by H.

Explicitly, one has: S τi , τj , τk = S τj i τki , where, from now on, we use the notation τj i = τj − τi . As we explicitly show in the appendix, the function S (x) can be computed exactly. It is a monotonically decreasing function defined on [0, 1] ranging from 1 to −1. It satisfies S (1 − x) = −S (x) and is explicitly given by S (x) = 1 − 2L (x) . The function L (x) is the so called normalized Rogers dilogarithm [57], defined in terms xn of the usual dilogarithm Li2 (x) = ∞ n=1 n2 as: L (x) = 6 1 Li2 (x) + ln (x) ln (1 − x) .

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Communications in Mathematical Physics - Volume 225 by M. Aizenman (Chief Editor)

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