Variational calculation of transport coefficients in diffusive lattice gases

摘要

A diffusive lattice gas is characterized by the diffusion coefficient depending only on the density. The Green-Kubo formula for diffusivity can be represented as a variational formula, but even when the equilibrium propertiesof a lattice gas are analytically known, the diffusion coefficient can be computed only in the exceptional situationwhen the lattice gas is gradient. In the general case, minimization over an infinite-dimensional space is required.We propose an approximation scheme based on minimizing over finite-dimensional subspaces of functions.The procedure is demonstrated for one-dimensional generalized exclusion processes in which each site canaccommodate at most two particles. Our analytical predictions provide upper bounds for the diffusivity that arevery close to simulation results throughout the entire density range. We also analyze nonequilibrium densityprofiles for finite chains coupled to reservoirs. The predictions for the profiles are in excellent agreement withsimulations.