Constructing useful statistical master equations for clusters

Models and computational experiments provide insights into ways to construct and use master equations to describe kinetics of very complex systems. The goal of the work is establishing reliable ways to create such equation systems for small statistical samples of very large complex systems, that are good mimics of their full but unmanageable counterparts. Two converging approaches are described: one is based on any of a set of very simplified models of a complex potential surface; the other is based on simplifying the representation of the realistic surface itself. The results from systems of moderate size indicate that optimism is justified, regarding attainment of the goal for very large systems.