  We investigate the role of entropic concepts for the relaxation dynamics in
granular systems. In these systems the existence of a geometrical frustration
induces a drastic modification of the allowed phase space, which in its turn
induces a dynamic behavior characterized by hierarchical relaxation phenomena
with several time scales associated. In particular we show how, in the
framework of a mean-field model introduced for the compaction phenomenon, there
exists a free-energy-like functional which decreases along the trajectories of
the dynamics and which allows to account for the asymptotic behavior: e.g.
density profile, segregation phenomena. Also we are able to perform the
continuous limit of the above mentioned model which turns out to be a diffusive
limit. In this framework one can single out two separate physical ingredients:
the free-energy-like functional that defines the phase-space and the asymptotic
states and a diffusion coefficient $D(\rho)$ accounting for the velocity of
approach to the asymptotic stationary states.
