Do granular systems obey statistical mechanics? A review of recent work assessing the applicability of equilibrium theory to vibrationally excited granular media

Driven granular media - assemblies of discrete, macroscopic elements exposed to a source of mechanical energy - represent inherently out-of-equilibrium systems. Although granular media are ubiquitous in both nature and industry, due to their dissipative nature and resultant complex behaviors they remain startlingly poorly understood as compared to classical, thermodynamic systems. Nonetheless, in recent years it has been observed that the behaviors of granular media can, under certain circumstances, closely resemble those of equilibrium systems. One of the most important contemporary questions in the field of granular physics is whether these similarities are merely superficial, or whether the parallels run deep enough that the behaviors of these nonequilibrium systems can in fact be successfully captured using analogs to existing theoretical models developed for classical systems. In this review, we draw together the findings of a variety of recent studies where this question has been addressed, comparing and contrasting the results and conclusions presented. We focus our attention on vibrated and vibrofluidized granular beds, which provide a canonical system representative of various equilibrium and nonequilibrium physical systems, and whose simple dynamics offer a valuable testing ground for exploring the fundamental physics of the granular state.