Numerical calculation of granular entropy

Asenjo, Daniel and Paillusson, Fabien and Frenkel, Daan (2014) Numerical calculation of granular entropy. Physical Review Letters, 112 (9). ISSN 0031-9007

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Abstract

We present numerical simulations that allow us to compute the number of ways in which N particles can pack into a given volume V. Our technique modifies the method of Xu, Frenkel, and Liu [Phys. Rev. Lett. 106, 245502 (2011)] and outperforms existing direct enumeration methods by more than 200 orders of magnitude. We use our approach to study the system size dependence of the number of distinct packings of a system of up to 128 polydisperse soft disks. We show that, even though granular particles are distinguishable, we have to include a factor 1/N! to ensure that the entropy does not change when exchanging particles between systems in the same macroscopic state. Our simulations provide strong evidence that the packing entropy, when properly defined, is extensive. As different packings are created with unequal probabilities, it is natural to express the packing entropy as S=−∑ipilnpi−lnN!, where pi denotes the probability to generate the ith packing. We can compute this quantity reliably and it is also extensive. The granular entropy thus (re)defined, while distinct from the one proposed by Edwards [J. Phys. Condens. Matter 2, SA63 (1990)], does have all the properties Edwards assumed.

Keywords:Granular Matter, Soft Matter, Entropy, NotOAChecked
Subjects:F Physical Sciences > F200 Materials Science
F Physical Sciences > F340 Mathematical & Theoretical Physics
G Mathematical and Computer Sciences > G400 Computer Science
Divisions:College of Science > School of Mathematics and Physics
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ID Code:17980
Deposited On:09 Sep 2015 05:10

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