Geometric and topological entropies of sphere packing
Here, we present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic and weakly underconstrained packings in 2D and 3D. The theory generalizes concepts of granular and glassy configurational entropies for the case of nonjammed systems. It is directly applicable to sticky colloids and predicts an asymptotic phase behavior of sticky spheres in the limit of strong binding.
- Research Organization:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- Grant/Contract Number:
- SC0012704
- OSTI ID:
- 1899905
- Report Number(s):
- BNL-223727-2022-JAAM
- Journal Information:
- Physical Review. E, Journal Name: Physical Review. E Journal Issue: 1 Vol. 105; ISSN 2470-0045
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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