  We show that the recently proposed interacting Ehrenfest M-urn model at
equilibrium can be exactly mapped to a mean-field M-state Potts model. By
exploiting this correspondence, we show that the M-state Potts model with M >=
3, with transition rates motivated by the non-equilibrium urn model, can
exhibit rich non-equilibrium spin dynamics such as non-equilibrium steady
states and non-equilibrium periodic states. Monte Carlo simulations of the
3-state Potts model are performed to demonstrate explicitly the first-order
transitions for the equilibrium and non-equilibrium steady states, as well as
the far-from-equilibrium periodic states.
