Measurement of granular entropy.

Recently, Dean and Lefèvre [Phys. Rev. Lett. 90, 198301 (2003)] developed a method for testing the statistical mechanical theory of granular packings proposed by Edwards and co-workers [Physica A 157, 1080 (1989); Phys. Rev. E 58, 4758 (1998)]. The method relies on the prediction that the ratio of two overlapping volume histograms should be exponential in volume. We extend the method by showing that one can also calculate the entropy of the packing and also that the method can yield false positive results when the histograms are Gaussians with nearly identical variances. We then apply the method to simulations and experiments of granular compaction. The distribution of global volumes (the volume of the entire packing) is nearly Gaussian and it is difficult to conclude if the theory is valid. On the other hand, the distribution of Voronoï volumes clearly obeys the theoretical prediction.