  The Edwards hypothesis of ergodicity of blocked configurations for gently
tapped granular materials is tested for abstract models of spin systems on
random graphs and spin chains with kinetic constraints. The tapping dynamics is
modeled by considering two distinct mechanisms of energy injection: thermal and
random tapping. We find that ergodicity depends upon the tapping procedure
(i.e. the way the blocked configurations are dynamically accessed): for thermal
tapping ergodicity is a good approximation, while it fails to describe the
asymptotic stationary state reached by the random tapping dynamics.
