  We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for
finitely many coupled phase oscillators with phase frustration. Whereas in the
thermodynamic limit coupled oscillators exhibit stationary states and a
constant order parameter, finite-size networks exhibit persistent temporal
fluctuations of the order parameter. These fluctuations are caused by the
interaction of the synchronized oscillators with the non-entrained oscillators.
We present numerical results suggesting that the collective effect of the
non-entrained oscillators on the synchronized cluster can be approximated by a
Gaussian process. This allows for an effective closed evolution equation for
the synchronized oscillators driven by a Gaussian process which we approximate
by a two-dimensional Ornstein-Uhlenbeck process. Our reduction reproduces the
stochastic fluctuations of the order parameter and leads to a simple stochastic
differential equation for the order parameter.
