Effective ergodicity breaking phase transition in a driven-dissipative system

The growing interest in non-equilibrium systems has prompted question of what equilibrium methods can be extended to non-equilibrium systems. We discuss a non-equilibrium phase transition in the Olami-Feder-Christensen model that is characterized by critical exponents which obey scaling laws from equilibrium statistical mechanics. Below the critical noise, the sites are trapped in different limit cycles. The probability distributions of different trajectories are distinct and highlight the non-ergodic nature of the phase. Above the critical noise all sites converge to the same time average and the system is effectively ergodic. We use tools from the study of glassy systems and nonlinear dynamics to illuminate various properties of this non-equilibrium phase transition. Our results show a promising start to extending the methods of equilibrium statistical mechanics to a new class of non-equilibrium systems.