Entropy in the Kuramoto model and its implications for the 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.