A deductive statistical mechanics approach for granular matter

TL;DR

This paper develops a deductive statistical mechanics framework for granular matter, revealing a universal density fluctuation distribution that aligns well with experimental and simulation data across various systems.

Contribution

It introduces a new theoretical approach for granular materials based on minimal physical assumptions, predicting a universal distribution for density fluctuations.

Findings

Universal density fluctuation distribution similar to Maxwell-Boltzmann.

Excellent quantitative agreement with experimental and simulation data.

Distribution characterized by a single parameter sensitive to structural changes.

Abstract

We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such a distribution is the equivalent of the Maxwell-Boltzmann's distribution in the kinetic theory of gasses. The comparison with a very extensive set of experimental and simulation data for packings of monosized spherical grains, reveals a remarkably good quantitative agreement with the theoretical predictions for the density fluctuations both at the grain level and at the global system level. Such agreement is robust over a broad range of packing fractions and it is observed in several distinct systems prepared by using different methods. The equilibrium distributions are characterized by only one parameter ($k$) which is a quantity very sensitive to changes in the structural organization. The thermodynamical equivalent of $k$ and its relation with the `granular temperature' are also discussed.