Ergodicity breaking and restoration in models of heat transport with microscopic reversibility

Abstract: The behavior of lattice models in which time reversibility is enforced at the level of trajectories (microscopic reversibility) is studied analytically. Conditions for ergodicity breaking are explored, and a few examples of systems characterized by an additional conserved quantity besides energy are presented. All the systems are characterized by ergodicity restoration when put in contact with a thermal bath, except for specific choices of the interactions between the atoms in the system and the bath. The study shows that the additional conserved quantities return to play a role in non-equilibrium conditions. The similarities with the behavior of some mesoscale systems, in which the transition rates satisfy detailed balance but not microscopic reversibility, are discussed.