Universality in driven Potts models.

We study the stochastic dynamics of infinitely many globally interacting units made of q states distributed uniformly along 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.