  Glass-forming systems, which are characterized by a highly disordered energy
landscape, have been studied in physics by a simulation-based state space
aggregation. The purpose of this article is to develop a path-independent
approach within the framework of aperiodic, reversible Markov chains with
exponentially small transition probabilities which depend on some energy
function. This will lead to the definition of certain metastates, also called
metabasins in physics. More precisely, our aggregation procedure will provide a
sequence of state space partitions such that on an appropriate aggregation
level certain properties (see Properties 1--4 of the Introduction) are
fulfilled. Roughly speaking, this will be the case for the finest aggregation
such that transitions back to an already visited (meta-)state are very unlikely
within a moderate time frame.
