Markov state model for exploring the long-time dynamics of glass formers

Extensive efforts have been dedicated towards establishing robust links between the structural and dynamical heterogeneity found in amorphous materials at the nanoscale. Markov state models (MSMs) offer the attractive possibility of coarse-graining the dynamics of complex systems into a low-dimensional space, in which transitions occur with rates corresponding to the slowest modes of the system. We construct a two-state MSM of a binary Lennard-Jones mixture using Graph Dynamical Neural Networks in combination with the Variational Principle for Markov Processes. The transition timescale of the MSM is more than an order of magnitude larger than the conventional alpha-relaxation time, and reveals a fragile to strong crossover at the glass transition. The learned map of states assigned to the particles exhibits correlations of a few molecular diameters that, remarkably, are completely insensitive to temperature. We show that the MSM effectively constructs a map of scaled excess Voronoi volume, and the free energy difference between the two states is given exactly by the entropy of the these distributions. These results resonate with classic free volume theories of the glass transition and single out local packing fluctuations as the slowest relaxing features.