Hydrodynamics in kinetically-constrained lattice-gas models

TL;DR

This paper investigates how kinetically-constrained lattice-gas models, used for glassy systems, exhibit nonlinear diffusion behavior out of equilibrium, revealing correlations that affect diffusion coefficients and extend to broader non-gradient models.

Contribution

It demonstrates that these models follow a nonlinear diffusion equation with a density-dependent coefficient and identifies the role of correlations in discrepancies between theory and simulations.

Findings

Diffusion in these models can be approximated by a nonlinear diffusion equation.

Correlations emerge out of equilibrium, affecting diffusion coefficient accuracy.

Similar correlation effects are observed under external forces in non-gradient models.

Abstract

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.