Universal Critical Behavior of Noisy Coupled Oscillators

TL;DR

This paper investigates the universal critical behavior of large systems of noisy coupled oscillators near a Hopf bifurcation, revealing a generic relation between correlation and response functions and a strong violation of fluctuation-dissipation relations.

Contribution

It provides a perturbative renormalization group analysis of the non-equilibrium critical point in coupled oscillators, highlighting universal properties and deviations from equilibrium relations.

Findings

Universal relation between correlation and response functions at criticality

Strong violation of fluctuation-dissipation relation

Critical behavior described by a statistical field theory

Abstract

We study the universal thermodynamic properties of systems consisting of many coupled oscillators operating in the vicinity of a homogeneous oscillating instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic critical point far from equilibrium described by a statistical field theory. We perform a perturbative renormalization group study, and show that at the critical point a generic relation between correlation and response functions appears. At the same time the fluctuation-dissipation relation is strongly violated.