Metabasins - a State Space Aggregation for highly disordered Energy Landscapes

TL;DR

This paper introduces a path-independent method for aggregating state spaces in highly disordered energy landscapes, defining metastates called metabasins within a Markov chain framework, to better understand glass-forming systems.

Contribution

It develops a novel, path-independent aggregation approach for Markov chains that defines metastates (metabasins) in disordered energy landscapes, fulfilling specific properties.

Findings

Provides a sequence of state space partitions satisfying key properties.

Ensures transitions back to visited states are very unlikely within moderate time.

Offers a framework applicable to glass-forming systems with complex energy landscapes.

Abstract

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.