A theory of supercooled-liquid dynamics based on machine-learned softness

Recent work has used machine learning to identify a local structural variable, the softness S, which is predictive of rearrangements in a variety of systems. In simulations of supercooled liquids and glasses, S has a simple interpretation in terms of local energy barriers to rearrangement, and is found to correlate well with the probability of particles to rearrange, both in and out of equilibrium.  Here we build a theory of the dynamics of supercooled liquids in terms of S.  By measuring the changes in S induced nearby when a particle rearranges in molecular dynamics simulations, we quantify facilitation. We describe a class of stochastic models which can incorporate these measurements, and show how time-reversal symmetry places strong restrictions on the parameters of the model.  This results in a theory of dynamics whose parameters are well-founded in microscopic measurements and which can be used to predict the growth of dynamical heterogeneity as the system is cooled.