Information geometry and synchronization phase transition in Kuramoto model
Statistical Mechanics
2023-05-03 v2 Disordered Systems and Neural Networks
High Energy Physics - Theory
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.
Cite
@article{arxiv.2211.15617,
title = {Information geometry and synchronization phase transition in Kuramoto model},
author = {Artem Alexandrov and Alexander Gorsky},
journal= {arXiv preprint arXiv:2211.15617},
year = {2023}
}
Comments
Revised version, matched with published