  We study the stochastic dynamics of infinitely many globally interacting
$q$-state units on a ring that is externally driven. While repulsive
interactions always lead to uniform occupations, attractive interactions give
rise to much richer phenomena: We analytically characterize a Hopf bifurcation
which separates a high-temperature regime of uniform occupations from a
low-temperature one where all units coalesce into a single state. For odd $q$
below the critical temperature starts a synchronization regime which ends via a
second phase transition at lower temperatures, while for even $q$ this
intermediate phase disappears. We find that interactions have no effects except
below critical temperature for attractive interactions. A thermodynamic
analysis reveals that the dissipated work is reduced in this regime, whose
temperature range is shown to decrease as $q$ increases. The $q$-dependence of
the power-efficiency trade-off is also analyzed.
