Consider the infinite particle system on the countable set $S$ with the simple exclusion interaction and one-particle motion determined by the stochastic transition matrix $p(x, y)$. In the past, the ergodic theory of this process has been treated successfully only when $p(x, y)$ is symmetric, in which case great simplifications occur. In this paper, coupling techniques are used to give a complete description of the set of invariant measures for the system in the following three cases: (a) $p(x, y)$ is translation invariant on the integers and has mean zero, (b) $p(x, y)$ corresponds to a birth and death chain on the nonnegative integers, and (c) $p(x, y)$ corresponds to the asymmetric simple random walk on the integers.
"Coupling the Simple Exclusion Process." Ann. Probab. 4 (3) 339 - 356, June, 1976. https://doi.org/10.1214/aop/1176996084