  We analyze a non-reversible mean-field jump dynamics for discrete q-valued
rotators and show in particular that it exhibits synchronization. The dynamics
is the mean-field analogue of the lattice dynamics investigated by the same
authors in [26] which provides an example of a non-ergodic interacting particle
system on the basis of a mechanism suggested by Maes and Shlosman [32]. Based
on the correspondence to an underlying model of continuous rotators via a
discretization transformation we show the existence of a locally attractive
periodic orbit of rotating measures. We also discuss global attractivity, using
a free energy as a Lyapunov function and the linearization of the ODE which
describes typical behavior of the empirical distribution vector.
