Measuring the configurational temperature of a binary disc packing

TL;DR

This paper evaluates four methods for measuring the configurational temperature in binary disc packings, finding only two agree and that the temperature behaves as an intensive variable only in sufficiently large samples.

Contribution

It compares four measurement methods for configurational temperature in granular packings and investigates the conditions under which it behaves as an intensive variable.

Findings

Only two of the four methods agree quantitatively.

Configurational temperature is intensive only for samples larger than ~200 particles.

Correlations between particle volumes influence the measurement of X.

Abstract

Jammed packings of granular materials differ from systems normally described by statistical mechanics in that they are athermal. In recent years a statistical mechanics of static granular media has emerged where the thermodynamic temperature is replaced by a configurational temperature X which describes how the number of mechanically stable configurations depends on the volume. Four different methods have been suggested to measure X. Three of them are computed from properties of the Voronoi volume distribution, the fourth takes into account the contact number and the global volume fraction. This paper answers two questions using experimental binary disc packings: First we test if the four methods to measure compactivity provide identical results when applied to the same dataset. We find that only two of the methods agree quantitatively. Secondly, we test if X is indeed an intensive variable; this becomes true only for samples larger than roughly 200 particles. This result is shown to be due to recently found correlations between the particle volumes [Zhao et al., Europhys. Lett., 2012, 97, 34004].