Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation
File(s)
Accepted version
Author(s)
Blumenfeld, R
Amitai, S
Jordan, JF
Hihinashvili, R
Type
Journal Article
Abstract
We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is unaffected by most of the configurational microstates. Consequently, the commonly used partition function underestimates the entropy severely. We then propose a new formulation, replacing the volume function with a connectivity function that depends on all the structural degrees of freedom and accounts correctly for the entire entropy. We discuss the advantages of the new formalism and derive explicit results for two- and three-dimensional systems. We test the formalism by calculating the entropy of an experimental two-dimensional system, as a function of system size, and showing that it is an extensive variable.
Date Issued
2016-04-04
Date Acceptance
2016-04-01
Citation
Physical Review Letters, 2016, 116 (14)
ISSN
0031-9007
Publisher
American Physical Society
Journal / Book Title
Physical Review Letters
Volume
116
Issue
14
Copyright Statement
© 2016 American Physical Society. Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation
Raphael Blumenfeld, Shahar Amitai, Joe F. Jordan, and Rebecca Hihinashvili
Phys. Rev. Lett. 116, 148001 – Published 4 April 2016
Raphael Blumenfeld, Shahar Amitai, Joe F. Jordan, and Rebecca Hihinashvili
Phys. Rev. Lett. 116, 148001 – Published 4 April 2016
Sponsor
Engineering & Physical Science Research Council (E
Grant Number
EP/H051716/1
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
FLUCTUATIONS
EQUIPARTITION
STATE
Publication Status
Published
Article Number
148001