Recently, the idea of an effective temperature of the slow modes of a dense liquids has attracted attention due to the fact that it can be applied to a variety of systems (Cugliandolo et al. 1997; Parisi 1997; Barrat & Kob 1999; Nicodemi 1999; Sciortino & Tartaglia 2001; Berthier & Barrat 2002; Ono et al. 2002). Makse & Kurchan (2002) showed that this parameter is equivalent to the FD relation between the mean square displacement (MSD) and mobility in a bi-disperse, gently sheared packing of compressible spheres. This indicates that a thermodynamical formalism for granular materials might be useful. This formalism is a generalization of the incompressible grain formalism proposed by Edwards & Oakeshott (1989).