Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy materials

In a recent article M. Merolle et al., Proc. Natl. Acad. Sci. U.S.A. 102, 10837 (2005)], it was argued that dynamic heterogeneity in d-dimensional glass formers is a manifestation of an order-disorder phenomenon in the d+1 dimensions of space time. By considering a dynamical analog of the free energy, evidence was found for phase coexistence between active and inactive regions of space time, and it was suggested that this phenomenon underlies the glass transition. Here we develop these ideas further by investigating in detail the one-dimensional Fredrickson-Andersen (FA) model, in which the active and inactive phases originate in the reducibility of the dynamics. We illustrate the phase coexistence by considering the distributions of mesoscopic space-time observables. We show how the analogy with phase coexistence can be strengthened by breaking microscopic reversibility in the FA model, leading to a nonequilibrium theory in the directed percolation universality class.