  We introduce and study a family of cooperative exclusion processes whose
microscopic dynamics is governed by selective kinetic constraints. They
display, in sharp contrast to the simple symmetric exclusion process, density
profiles that can be concave, convex or both, depending on the density of
boundary particle reservoirs. A mean-field analysis based on a diffusion
equation with a density-dependent diffusion coefficient qualitatively
reproduces this behaviour, and suggests its occurrence in liquids with a
diffusivity anomaly.
