We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the "giant component" according to the Erdos-Renyi theorem. Copyright (C) EPLA, 2015
A geometric entropy detecting the Erdos-Renyi phase transition
Franzosi Roberto;
2015
Abstract
We propose a method to associate a differentiable Riemannian manifold to a generic many-degrees-of-freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical statistical mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the "giant component" according to the Erdos-Renyi theorem. Copyright (C) EPLA, 2015File in questo prodotto:
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