A basis for the statistical mechanics of granular systems

This chapter highlights the use of statistical mechanics tools in situations where the system is out of equilibrium and jammed. The chapter illustrates the derivation of Boltzmann equation for a jammed granular system and shows that the Boltzmann's analysis can be used to produce a "Second Law" for jammed systems. In a thermal system, the Brownian motion of the constituent particles implies that the system dynamically explores the available energy landscape, such that the notion of a statistical ensemble applies. For densely packed systems in which enduring contacts between particles are important, the potential energy barrier prohibits an equivalent random motion. At first sight it seems that the thermal statistical mechanics do not apply to these systems as there is no mechanism for averaging over the configurational states. Hence, these systems are inherently out of equilibrium. The chapter highlights the fundamental questions in this area of physics and points out the key quantities in characterizing a packing of particles, accessible through a novel experimentation method that is also presented.