Stationary coalescing walks on the lattice II: entropy
Stationary coalescing walks on the lattice II: entropy
复制标题
晶格上的静止聚结行走 II：熵
作者：
J. Chaika;Arjun Krishnan
本文是Chaika和Krishnan，2016的续篇。我们再次考虑整数格Zd上最近邻半无限游动族的平移不变测度。我们假设一旦行走相遇，它们就合并。我们考虑这些系统的各种熵性质。我们表明，在完全正熵的系统中，双无限轨道必须携带熵。在2维定向行走的情况下，我们证明了正熵保证所有轨迹不可能是双无限的。为了证明我们的定理是正确的，我们构造了一个平稳的离散时间对称排斥过程，其粒子轨道形成携带熵的双无限轨道。
This paper is a sequel to Chaika and Krishnan, 2016. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Zd . We assume that once walks meet, they coalesce. We consider various entropic properties of these systems. We show that in systems with completely positive entropy, bi-infinite trajectories must carry entropy. In the case of directed walks in dimension 2 we show that positive entropy guarantees that all trajectories cannot be bi-infinite. To show that our theorems are proper, we construct a stationary discrete-time symmetric exclusion process whose particle trajectories form bi-infinite trajectories carrying entropy.