See NonEq statmech notes.

Also:

http://www-sop.inria.fr/members/Olivier.Faugeras/MVA/ArticlesALire09/acebron-bonilla-etal-05.pdf

http://arxiv.org/pdf/1403.2083v2.pdf

https://en.wikipedia.org/wiki/Kuramoto_model

Things to note:

We transform in most manipulations (including in notes) to a frame that rotates with angular frequency equal to the mean angular frequency of oscillators, $\langle \omega \rangle$.

In this frame, the assumption is that the phase of the order parameter, $\psi$ is constant, and so can be chosen to $0$.

The fact that it is constant is used to deduce that for the non-phase-locked oscillators (in case of partial coherence) their probability distribution must be constant, so that they are in a state of dynamic equilibrium (because their drift velocity $v$ can't be $0$ as for the phase-locked states).

These differences in behaviour between phase-locked and non-phase-locked oscillators comes from solving their dynamical equations (eq. (9) in this paper, the behavior of which depends on the parameter $\omega_i/(Kr_{st})$.