  This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again
consider translation invariant measures on families of nearest-neighbor
semi-infinite walks on the integer lattice Z^d. 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.
