Glassy Behaviours in A-Thermal Systems, the Case of Granular Media: A Tentative Review

Abstract

Granular media, commonly referred to as a-thermal systems, obey a dissipative dynamics a priori very different from an Hamiltonian evolution. However everyday life and recent experiments suggest that a thermodynamical description of granular media might be feasible. Especially in the context of gentle compaction of grains, strong similarities with the behaviour of thermal glassy systems have been underlined. Given that granular media consist in a large number of grains, there is a strong motivation for providing a statistical ground to this hypothetic thermo- dynamical description. It has been argued by Edwards and collaborators that the dynamics is controlled by the mechanically stable - the so-called blocked - configu- rations and that all such configurations of a given volume are statistically equivalent. This immediately leads to the definition of a configurational entropy and the associ- ated state variable, the "compactivity", the formal analogy of a temperature. First attempts to test this flat measure assumption have been conducted. However, clear evidence in real granular media is still lacking. In this lecture, we shall first discuss the meaning of thermal vs. a-thermal systems, second review old and new results revealing the strong similarities between granular media close to the jamming tran- sition and super-cooled liquids close to the glass transition, and finally present and discuss Edwards proposal, together with recent experimental results on the volume statistics inside a granular packing.