We consider infinite particle systems on a countable set $S$ with two-particle exclusion-eating motion determined by a symmetric transition function $p(x, y)$. This is, in a certain sense, a mixture of the exclusion process and the voter model. We discuss the dual process of this process and use the dual process to give a description of the set of invariant measures and to prove an ergodic theorem.
"Symmetric Two-Particle Exclusion-Eating Processes." Ann. Probab. 23 (3) 1439 - 1455, July, 1995. https://doi.org/10.1214/aop/1176988191