  We introduce the mathematical theory of the particle systems that interact
via permutations, where the transition rates are assigned not to the jumps from
a site to a site, but to the permutations themselves. This permutation
processes can be viewed as a generalization of the symmetric exclusion
processes, where particles interact via transpositions. The duality and
coupling techniques for the processes are described, the needed conditions for
them to apply are established. The stationary distributions of the permutation
processes are explored for translation invariant cases.
