A geometric entropy detecting the Erdös-Rényi phase transition
Authors: Franzosi R., Felice D., Mancini S., Pettini M.
Autors Affiliation: QSTAR and INO-CNR, Largo E. Fermi 2, Firenze, 50125, Italy; School of Science and Technology, University of Camerino, Camerino, 62032, Italy; INFN-Sezione di Perugia, Via A. Pascoli, Perugia, 06123, Italy; Aix-Marseille University, Marseille, France; CNRS, Centre de Physique Théorique, UMR7332, Marseille, 13288, 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
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: 10.1209/0295-5075/111/20001Citations: 11data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2021-10-10References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here