Entropy in the Kuramoto model and its implications for the stability of partially synchronized states

TL;DR

This paper explores how entropy behaves in the infinite-N Kuramoto model, revealing that entropy's evolution depends on the synchronization state and providing insights into the stability of partially synchronized states.

Contribution

It introduces an entropy functional for the Kuramoto model, derives its time derivative, and discusses implications for the stability of synchronized states.

Findings

Entropy's time derivative depends on the order parameter

Entropy is non-increasing without diffusion

Insights into stability of partially synchronized states

Abstract

We discuss the concept of entropy applied to the infinite-N Kuramoto model and derive an expression for its time derivative. The time derivative of the entropy functional is shown to depend on the synchronization order parameter in a very simple way and, absent diffusion, it is never increasing. The implications of this for the stability of partially synchronized states is discussed. We conclude with a section on the entropy of the marginal density function averaged over all natural frequencies.