  We investigate the diffusion coefficient of the time integral of the Kuramoto
order parameter in globally coupled nonidentical phase oscillators. This
coefficient represents the deviation of the time integral of the order
parameter from its mean value on the sample average. In other words, this
coefficient characterizes long-term fluctuations of the order parameter. For a
system of N coupled oscillators, we introduce a statistical quantity D, which
denotes the product of N and the diffusion coefficient. We study the scaling
law of D with respect to the system size N. In other well-known models such as
the Ising model, the scaling property of D is D \sim O(1) for both coherent and
incoherent regimes except for the transition point. In contrast, in the
globally coupled phase oscillators, the scaling law of D is different for the
coherent and incoherent regimes: D \sim O(1/N^a) with a certain constant a>0 in
the coherent regime and D \sim O(1) in the incoherent regime. We demonstrate
that these scaling laws hold for several representative coupling schemes.
