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 $Q^\ast$ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function of Speedy yields a new form for the $d$-dimensional partition function, $Q(N,V,T)=Q^\ast \exp(-N \mathcal{J})$, where $\mathcal{J}$ depends strictly on the boundary-to-volume ratio of the voids and the close-packing density. Overall, this work deepens our statistical geometric understanding of the hard-sphere system.
From: Luke K. Davis [view email]
[v1]
Mon, 15 Jun 2026 09:50:31 UTC (9,261 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。