Kinetically constrained models are lattice gas models used to describe glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between 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 the perturbation. We find that under the proper coarse-graining, the behavior of these models may be expressed as a 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 infinitesimally. Similar correlations appear when the system is driven out of equilibrium by applying a force in a particular direction [1]. 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.

[1] F. Turci, E. Pitard, and M. Sellitto, Phys. Rev. E 86, 031112 (2012)