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Amorphous materials exhibit structural heterogeneities that relax only onlong timescales. Using machine learning techniques, we construct a Markov statemodel (MSM) for model glass formers that coarse-grains the dynamics into alow-dimensional space, in which transitions occur with rates corresponding tothe slowest modes of the system. The transition timescale between states ismore than an order of magnitude larger than the conventional alpha-relaxationtime, and reveals a fragile to strong crossover at the glass transition. Thelearned map of states assigned to the particles exhibits correlations of a fewmolecular diameters both at liquid and glassy temperatures. We show that theMSM effectively constructs a map of scaled excess Voronoi volume, and the freeenergy difference between the two states is given exactly by the entropy of thethese distributions. These results resonate with classic free volume theoriesof the glass transition, singling out local packing fluctuations as the slowestrelaxing features.

Exploring glassy dynamics with Markov state models from graph dynamical neural networks