Description
In the study of interacting particle systems duality is an important
tool used to prove various types of long-time behavior, for example convergence to an invariant distribution. The two most used types of dualities
are additive and cancellative dualities, which we are able to treat in a unified framework considering commutative monoids (i.e.\ semigroups containing a neutral element) as cornerstones of such a duality. For interacting particle systems on local state spaces with more than two elements this approach revealed formerly unknown dualities.
As an application of one of the newly found dualities a convergence result of a combination of the \emph{contact process} and its cancellative version, formerly known as the \emph{annihilating branching process}, is presented.
