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Attractor Properties for Irreversible and Reversible Interacting Particle Systems by Jahnel, Benedikt; Kuelske, Christof is a scholarly article available to read on EtoBox.

What is Attractor Properties for Irreversible and Reversible Interacting Particle Systems about?

We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild non-degeneracy conditions. We prove that weak limit points of any trajectory of translation-invariant measures, satisfying a non-nullness condition, are Gibbs states for the same specification as the time-stationary measure. This is done under the additional assumption that zero entropy loss of the limiting measure w.r.t. the time-stationary measure implies that they are Gibbs measures for the same specification. We show how to prove the non-nullness for a large number of cases, and also give an alternate version of the last condition such that the non-nullness requirement can be dropped. As an application we obtain the attractor property if there is a reversible Gibbs measure. Our method generalizes convergence results using relative entropy techniques to a large class of dynamics including irreversible and non-ergodic ones.

Author

Jahnel, Benedikt; Kuelske, Christof

Published

2015

Language

EN