Nonequilibrium first-order transition in coupled oscillator systems with inertia and noise

TL;DR

This paper investigates a coupled oscillator system with inertia and noise, revealing a nonequilibrium first-order phase transition between synchronized and incoherent states, with detailed phase diagrams and stability analysis.

Contribution

It provides the first comprehensive phase diagram for the model including inertia and noise, and demonstrates the first-order transition with analytical and numerical evidence.

Findings

System undergoes a nonequilibrium first-order phase transition.

Existence of metastable states with exponential escape times.

Recovery of the Kuramoto model transition in the zero noise and inertia limit.

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.