The Statistical Physics of Athermal Materials

Abstract

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.

Configurational entropy and effective temperature in systems of active Brownian particles

“…In Fig. [43][44][45] However, as it becomes more difficult to measure the effective temperature for larger system sizes, it would be interesting for future work to employ more precise methodologies to calculate the system size dependence of the effective temperature. 4a suggests that these active systems are non-extensive, which would be in agreement with previous studies on granular matter, where extensivity has been investigated using similar approaches.…”

An experimental investigation of the force network ensemble

“…To make predictions for the physical behavior of granular systems, tools and concepts from statistical physics have become widely used [5], but what is the correct ensemble to describe jammed granular packings? To get more insight into these jammed packings one needs to look at the structure of force networks that form in loaded granular packings.…”

Why granular media are thermal after all

“…Both results have contributed to the widespread believe in the physics community that grains may generally be approximated as elementary. Starting from this believe, "athermal statistical mechanics" (ASM) defines a reduced entropy S g that does not contain any microscopic degrees of freedom, only those of granular configurations, and assumes it is maximal in equilibrium [1]. One example is the Edward entropy, S Ed , given by the number of possibilities grains may be stably packed [2,3].…”