DYNAMICAL GIBBS VARIATIONAL PRINCIPLES FOR IRREVERSIBLE INTERACTING PARTICLE SYSTEMS WITH APPLICATIONS TO ATTRACTOR PROPERTIES
成果类型：
Article
署名作者：
Jahnel, Benedikt; Koeppl, Jonas
署名单位：
Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/22-AAP1926
发表日期：
2023
页码：
4570-4607
关键词：
摘要：
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.
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