Information geometry and synchronization phase transition in Kuramoto model

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.