Information geometry and synchronization phase transition in Kuramoto model

TL;DR

This paper explores the connection between the Kuramoto model's synchronization transition and information geometry, showing that the Fisher information metric diverges at criticality, serving as an alternative order parameter.

Contribution

It introduces a geometric perspective on the Kuramoto model, relating its dynamics to hyperbolic space and information geometry, and proposes Fisher information as a new indicator of phase transition.

Findings

Fisher information metric diverges at the critical point

Kuramoto model dynamics correspond to gradient flow of Kullback-Leibler divergence

Geometric approach provides new insights into synchronization phase transition

Abstract

We discuss the recently proposed description of Kuramoto model in terms of hyperbolic space and relate it to the information geometry. In particular the dynamical equation in Kuramoto all-to-all model is identified with the gradient flow of the Kullback-Leibner divergence on the statistical manifold. The Fisher information metric is evaluated for the Kuramoto and Kuramoto-Shakagichi models. We argue that the components of Fisher metric diverge at the critical point hence it can be used as an alternative order parameter for the synchronization phase transition.