  At the core of equilibrium statistical mechanics lies the notion of
statistical ensembles: a collection of microstates, each occurring with a given
a priori probability that depends only on a few macroscopic parameters such as
temperature, pressure, volume, and energy. In this review article, we discuss
recent advances in establishing statistical ensembles for athermal materials.
The broad class of granular and particulate materials is immune from the
effects of thermal fluctuations because the constituents are macroscopic. In
addition, interactions between grains are frictional and dissipative, which
invalidates the fundamental postulates of equilibrium statistical mechanics.
However, granular materials exhibit distributions of microscopic quantities
that are reproducible and often depend on only a few macroscopic parameters. We
explore the history of statistical ensemble ideas in the context of granular
materials, clarify the nature of such ensembles and their foundational
principles, highlight advances in testing key ideas, and discuss applications
of ensembles to analyze the collective behavior of granular materials.
