  We consider irreversible translation-invariant interacting particle systems
on the $d$-dimensional cubic 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 w.r.t. 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 w.r.t. the same
specification as the time-stationary measure. This extends previously known
results to fairly general irreversible interacting particle systems.
