Probability distribution of inherent states in models of granular media and glassesA. Coniglio1, A. Fierro1 and M. Nicodemi1, 2
1 Dipartimento di Scienze Fisiche, INFM and INFN Napoli, Complesso Universitario di Monte Sant'Angelo, Via Cintia, I-80126 Napoli, Italy
2 Department of Mathematics, Imperial College, London, SW7 2BZ, UK
(Received 19 March 2002 and Received in final form 14 June 2002 / Published online: 23 December 2002)
The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a "tap dynamics" analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new "thermodynamical" parameters, called "configurational temperatures" (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single "configurational temperature". Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed.
05.20.-y - Classical statistical mechanics.
75.10.Nr - Spin-glass and other random models.
81.05.Rm - Porous materials; granular materials.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002