A geometric entropy detecting the Erdös-Rényi phase transition

Year: 2015

Authors: Franzosi R., Felice D., Mancini S., Pettini M.

Autors Affiliation: QSTAR, I-50125 Florence, Italy; INO CNR, I-50125 Florence, Italy; Univ Camerino, Sch Sci & Technol, I-62032 Camerino, Italy; INFN Sez Perugia, I-06123 Perugia, Italy; Aix Marseille Univ, Marseille, France; CNRS, Ctr Phys Theor, UMR7332, F-13288 Marseille, France.

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, 2015

Journal/Review: EUROPHYSICS LETTERS

Volume: 111      Pages from: 20001-p1  to: 20001-p6

More Information: We acknowledge the financial support of the European Commission by the FET-Open grant agreement TOP-DRIM, No. FP7-ICT-318121.
DOI: 10.1209/0295-5075/111/20001

Citations: 11
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