Irreversible random and cooperative process on lattices: Direct determination of density expansions

For processes where events occur irreversibly, and in general cooperatively, at the sites of a lattice, hierarchies of rate equations for the probabilities of configurations of events can be written down immediately, provided the cooperative effects have finite range. Mostly truncation methods of solution have been implemented. Here we present a direct method of determination of formal “density” expansions and investigate some properties of the solution of these hierarchies. The basic technique is demonstrated by several explicit examples and is readily applied to handle lattices which are finite, semi-infinite, of infinite; uniform, periodic or with “defective” sites and to processes involving monomer or polyatomic filling or competing events.