Entropy for relaxation dynamics in granular media

We investigate the role of entropic concepts for the relaxation dynamics in granular systems. In particular, we show howl in the framework of a mean-h eld model introduced for compaction phenomenon. there exists a free-energy- like functional which decreases along the trajectories of the dynamics and which allows one to account for the asymptotic behavior: e.g., density prof ile, segregation phenomena. Also we are able to perform the continuous limi t 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 fr ee-energy-like functional that defines the phase space and the asymptotic s tates and a diffusion coefficient D(rho) accounting for the velocity of app roach to the asymptotic stationary states.