  Kinetically-constrained models are lattice-gas models that are used for
describing glassy systems. By construction, their equilibrium state is trivial
and there are no equal-time correlations between the occupancy of different
sites. We drive such models out of equilibrium by connecting them to two
reservoirs of different densities, and measure the response of the system to
this perturbation. We find that under the proper coarse-graining, the behavior
of these models may be expressed by a nonlinear diffusion equation, with a
model- and density-dependent diffusion coefficient. We find a simple
approximation for the diffusion coefficient, and show that the relatively mild
discrepancy between the approximation and our numerical results arises due to
non-negligible correlations that appear as the system is driven out of
equilibrium, even when the density gradient is infinitesimally small. Similar
correlations appear when such kinetically-constrained models are driven out of
equilibrium by applying a uniform external force. We suggest that these
correlations are the reason for the same discrepancy between the approximate
diffusion coefficient and the numerical results for a broader group of models,
non-gradient lattice-gas models, for which kinetically-constrained models are
arguably the simplest example thereof.
