Numerical Calculation of Granular Entropy
Physical Review Letters
American Physical Society
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Asenjo, D., Paillusson, F., & Frenkel, D. (2014). Numerical Calculation of Granular Entropy. Physical Review Letters, 112 https://doi.org/10.1103/PhysRevLett.112.098002
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.
This work has been supported by the EPSRC grant N EP/I000844/1. D.F. acknowledges support from ERC Advanced Grant 227758, Wolfson Merit Award 2007/R3 of the Royal Society of London. D.A. acknowledges support from Becas Chile CONICYT.
Royal Society (wm072834)
European Research Council (227758)
External DOI: https://doi.org/10.1103/PhysRevLett.112.098002
This record's URL: https://www.repository.cam.ac.uk/handle/1810/245233
Attribution-NonCommercial 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc/2.0/uk/
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