论文标题
不可逆的相互作用粒子系统与吸引力属性的应用的动态吉布斯变化原理
Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties
论文作者
论文摘要
我们考虑在$ d $二维的立方晶格上具有有限的局部状态空间的不可逆转的翻译不变的相互作用粒子系统，该晶格至少承认一个Gibbs量度作为时间阶段的度量。在一些轻度的退化条件下，我们证明的速率和规范，零相对熵损失的转换不变措施意味着该措施是Gibbs W.R.T.与时刻吉布斯测量的规范相同。作为一种应用，我们获得了不可逆的相互作用粒子系统的吸引子属性，该系统说，任何翻译不变量的轨迹的弱极限点都是Gibbs Measure W.R.T.与时刻度量相同的规范。这将先前已知的结果扩展到相当不可逆转的相互作用粒子系统。
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.
