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Stochastic interdependence of a probablility distribution on a product space is measured by its Kullback-Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed(More)
We present numerical and analytical evidence for a rst-order phase transition of the ferromagnetic spin chain with partition function Z() = (? 1)==() at the inverse temperature cr = 2. In a recent paper 6] we established a link between analytic number theory and classical statistical mechanics by interpreting the quotient Z(s) = (s ? 1)==(s) of Riemann zeta(More)
We analyze the number-theoretical spin chain with partition function Z() = (? 1)==() using the polymer model technique. The nite (grand) canonical chains give bounds for the limit free energy and internal energy. The correlation functions for inverse temperature = ?1 are products of two-point functions. A combinatorial result for general interval graphs is(More)
We review the notion of dynamical entropy by Connes, Narnhofer and Thirring and relate it to Quantum Chaos. A particle in a periodic potential is used as an example. This is worked out in the classical and the quantum mechanical framework, for the single particle as well as for the corresponding gas. The comparison does not only support the general(More)