PreprintCC BY-NC-SA 4.0arXiv
Geometric decomposition of the d-dimensional hard-sphere partition function
Abstract
We introduce a geometric decomposition of the hard-sphere partition function. Using a close-packing-inspired geometric bound on the available insertion volume, made rigorous when a corresponding local density certificate is available, we establish a reference upper bound Q∗ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function found by Speedy yields a new form for the d-dimensional partition function, Q(N,V,T)=Q∗ exp(−N 𝒥), where 𝒥 depends strictly on the boundary-to-volume ratio of the voids and the close-packing density. Overall, this work provides an exact reformulation of hard-sphere thermodynamics, thus deepening our statistical geometric understanding of hard spheres.
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BibTeX
@misc{davis2026geometric,
title = {{Geometric decomposition of the d-dimensional hard-sphere partition function}},
author = {Luke K. Davis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.16483},
eprint = {2606.16483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16483},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Geometric decomposition of the d-dimensional hard-sphere partition function
AU - Luke K. Davis
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2606.16483
UR - https://arxiv.org/abs/2606.16483
AB - We introduce a geometric decomposition of the hard-sphere partition function. Using a close-packing-inspired geometric bound on the available insertion volume, made rigorous when a corresponding local density certificate is available, we establish a reference upper bound Q^∗ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function found by Speedy yields a new form for the d-dimensional partition function, Q(N,V,T)=Q^∗ exp(−N 𝒥), where 𝒥 depends strictly on the boundary-to-volume ratio of the voids and the close-packing density. Overall, this work provides an exact reformulation of hard-sphere thermodynamics, thus deepening our statistical geometric understanding of hard spheres.
ER -