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: 10.1209/0295-5075/111/20001Citations: 11data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-12-08References taken from IsiWeb of Knowledge: (subscribers only)Connecting to view paper tab on IsiWeb: Click hereConnecting to view citations from IsiWeb: Click here