Titlebook: Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics; Marco Pettini Book 2007 Springer-Verlag New York 2007 Dynamics.Ge

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Topological Hypothesis on the Origin,ly singular behavior at the transition point. Moreover, we have seen that the presence of a singularity in the statistical-mechanical fluctuations of the curvature at the transition point has been proved analytically for the mean-field . model.

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Introduction,hase transitions. The mathematical concepts and methods used are borrowed from Riemannian geometry and from elementary differential topology, respectively. The new approach proposed also unveils deep connections between the two mentioned topics.

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Background in Physics,between them..The general problem of statistical physics is the following. Given a collection–in general a large collection–of atoms or molecules, given the interaction laws among the constituents of this collection of particles, and given the dynamical evolution laws, how can we predict the macrosc

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Geometrization of Hamiltonian Dynamics, system, that is, a system of particles interacting through forces derived from a potential, i.e., of the form (1.1), belongs to this class. The trajectories of a standard system can be seen as geodesics of a suitable Riemannian manifold. This classical result is based on the variational formulation