title: Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise.
abstract: We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques (UMR CNRS 8626), Université Paris-Sud, Orsay, France.
authors.forename: Shamik
authors.initials: S
authors.lastname: Gupta
authors.affiliation: Health and Technology Department, Istituto Superiore di Sanità, and INFN Sezione Roma1, Gruppo Collegato Sanità, Roma, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Campa
authors.affiliation: Department of Physics and Astronomy and CSDC, University of Florence, CNISM and INFN, via G. Sansone, 1 50019 Sesto Fiorentino, Italy.
authors.forename: Stefano
authors.initials: S
authors.lastname: Ruffo
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D044367:Phase Transition