Abstract
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 . 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.
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