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Stochastic lattice gases with degenerate rates, namely conservative particlesystems where the exchange rates vanish for some configurations, have beenintroduced as simplified models for glassy dynamics. We introduce twoparticular models and consider them in a finite volume of size $\ell$ incontact with particle reservoirs at the boundary. We prove that, as fornon--degenerate rates, the inverse of the spectral gap and the logarithmicSobolev constant grow as $\ell^2$. It is also shown how one can obtain, via ascaling limit from the logarithmic Sobolev inequality, the exponential decay ofa macroscopic entropy associated to a degenerate parabolic differentialequation (porous media equation). We analyze finally the tagged particledisplacement for the stationary process in infinite volume. In dimension largerthan two we prove that, in the diffusive scaling limit, it converges to aBrownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure

Exclusion Processes with Degenerate Rates: Convergence to Equilibrium and Tagged Particle