Universal splitting of nonequilibrium phase transitions in driven Potts heat engines

Abstract

We investigate nonequilibrium phase transitions and thermodynamic properties of driven Potts models coupled to two thermal reservoirs at different temperatures. The interplay with the multi-state structure of the Potts model leads to distinct phase-transition scenarios. The proposed driving scheme breaks the symmetry between the Potts states and gives rise to multiple transitions within the ordered phases, where the phases are characterized by different numbers of stable fixed points. This number can vary from $q$ fixed points to $1$ fixed point, corresponding to $q-1$ distinct transitions. The driving scheme strongly affects the thermodynamic operation regimes, allowing the system to operate as a heat engine. We demonstrate that these phenomena persist for both a mean-field (MF) model and a two-dimensional model, confirming the robustness of the results with respect to dimensionality. For the MF case, we also develop a phenomenological description in the strongly ordered regime that yields analytical expressions for the power, heat currents, and efficiency. Our results show how multi-state collective interactions, nonequilibrium driving, and thermal bias jointly generate a rich phase structure and the emergence of a collective heat engine.