Title: Bulk diffusion in a kinetically constrained lattice gas,
Abstract: In the hydrodynamic regime, the evolution of a stochastic lattice gas with
symmetric hopping rules is described by a diffusion equation with
density-dependent diffusion coefficient encapsulating all microscopic details
of the dynamics. This diffusion coefficient is, in principle, determined by a
Green-Kubo formula. In practice, even when the equilibrium properties of a
lattice gas are analytically known, the diffusion coefficient cannot be
computed except when a lattice gas additionally satisfies the gradient
condition. We develop a procedure to systematically obtain analytical
approximations for the diffusion coefficient for non-gradient lattice gases
with known equilibrium. The method relies on a variational formula found by
Varadhan and Spohn which is a version of the Green-Kubo formula particularly
suitable for diffusive lattice gases. Restricting the variational formula to
finite-dimensional sub-spaces allows one to perform the minimization and gives
upper bounds for the diffusion coefficient. We apply this approach to a
kinetically constrained non-gradient lattice gas, viz. to the Kob-Andersen
model on the square lattice.