  In supercooled liquids, dynamical facilitation refers to a phenomenon where
microscopic motion begets further motion nearby, resulting in spatially
heterogeneous dynamics. This is central to the glassy relaxation dynamics of
such liquids, which show super-Arrhenius growth of relaxation timescales with
decreasing temperature. Despite the importance of dynamical facilitation, there
is no theoretical understanding of how facilitation emerges and impacts
relaxation dynamics. Here, we present a theory that explains the microscopic
origins of dynamical facilitation. We show that dynamics proceeds by localized
bond-exchange events, also known as excitations, resulting in the accumulation
of elastic stresses with which new excitations can interact. At low
temperatures, these elastic interactions dominate and facilitate the creation
of new excitations near prior excitations. Using the theory of linear
elasticity and Markov processes, we simulate a model, which reproduces multiple
aspects of glassy dynamics observed in experiments and molecular simulations,
including the stretched exponential decay of relaxation functions, the
super-Arrhenius behavior of relaxation timescales as well as their
two-dimensional (2D) finite-size effects. The model also predicts the
subdiffusive behavior of the mean squared displacement (MSD) on short,
intermediate timescales. Furthermore, we derive the phonon contributions to
diffusion and relaxation, which when combined with the excitation contributions
produce the two-step relaxation processes, and the
ballistic-subdiffusive-diffusive crossover MSD behaviors commonly found in
supercooled liquids.
