110 citations · 918 across the 48 of their papers we have counts for
6 papers · 1 filter
Catching homologies by geometric entropy
D. Felice, R. Franzosi, S. Mancini +1
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for mea…
A geometric entropy detecting the Erdös-Rényi phase transition
Roberto Franzosi, Domenico Felice, Stefano Mancini +1
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, i…
Riemannian-geometric entropy for measuring network complexity
Roberto Franzosi, Domenico Felice, Stefano Mancini +1
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry…
Topology and Phase Transitions II. Theorem on a necessary relation
Roberto Franzosi, Marco Pettini
In this second paper, we prove a necessity Theorem about the topological origin of phase transitions. We consider physical systems described by smooth microscopic interaction poten…
Topology and Phase Transitions I. Preliminary Results
Roberto Franzosi, Marco Pettini, Lionel Spinelli
In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase trans…
Topology and Phase Transitions: Theorem on a necessary relation
Roberto Franzosi, Marco Pettini, Lionel Spinelli
An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601,…