Finite-size effects in a stochastic Kuramoto model.

We present a collective coordinate approach to study the collective behaviour of a finite ensemble of N stochastic Kuramoto oscillators using two degrees of freedom: one describing the shape dynamics of the oscillators and one describing their mean phase. Contrary to the thermodynamic limit N → ∞ in which the mean phase of the cluster of globally synchronized oscillators is constant in time, the mean phase of a finite-size cluster experiences Brownian diffusion with a variance proportional to 1/N. This finite-size effect is quantitatively well captured by our collective coordinate approach.