A geometric entropy detecting the Erdös-Rényi phase transition

Year: 2015

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

Journal/Review: EPL

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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