Non-equilibrium dynamics and phase transitions in Potts model and interacting Ehrenfest urn model

We show that the recently proposed interacting Ehrenfest M -urn model at equilibrium (Cheng et al., 2020) 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.