Counting metastable states in a kinetically constrained model using a patch repetition analysis.

We analyze metastable states in the East model, using a recently proposed patch repetition analysis based on time-averaged density profiles. The results reveal a hierarchy of states of varying lifetimes, consistent with previous studies in which the metastable states were identified and used to explain the glassy dynamics of the model. We establish a mapping between these states and configurations of systems of hard rods, which allows us to analyze both typical and atypical metastable states. We discuss connections between the complexity of metastable states and large-deviation functions of dynamical quantities, both in the context of the East model and more generally in glassy systems.