Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties

In this talk, we consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that the measure is Gibbs with respect to the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure with respect to the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems and joined work with Jonas Köppl.