We prove, using results for hydrodynamic limits,that an exclusion process starting from an ergodic initial distribution converges to product measure in one dimension. Our only assumption is the existence of a nonzero mean for the underlying random walk.
"An extension of a result of Andjel." Ann. Appl. Probab. 11 (2) 405 - 418, May 2001. https://doi.org/10.1214/aoap/1015345297