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

TL;DR

This paper analytically investigates ergodicity breaking and restoration in lattice models with microscopic reversibility, highlighting the role of conserved quantities and conditions affecting ergodic behavior in contact with thermal baths.

Contribution

It provides a theoretical analysis of ergodicity phenomena in reversible lattice models, including conditions for breaking and restoring ergodicity with conserved quantities.

Findings

Ergodicity is generally restored when models are coupled to a thermal bath.

Specific interactions can prevent ergodicity restoration.

Additional conserved quantities influence non-equilibrium behavior.

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.