2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66759We consider inhomogeneous Bernoulli measures of the form $\prod_{x\inΛ} p_x$ where $p_x$ are prescribed and uniformly bounded above and below away from 0 and 1. A comparison inequality is proved between the Kawasaki and Bernoulli-Laplace Dirichlet forms. Together with a recent result of Caputo on the gap of the Bernoulli-Laplace model, this proves a spectral gap of the correct order L^{-2} on cubes of side length L for the Kawasaki dynamics. The two block estimate of hydrodynamic limits is also obtained.Probability60K35; 60K37text