Metabasins - a State Space Aggregation for highly disordered Energy Landscapes

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.