Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-09-29
Physics
Condensed Matter
Statistical Mechanics
12 pages, 11 figures, v2: new section, appendix and references, plus some other minor changes; to be published in Phys. Rev. E
Scientific paper
We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to certain distance of other, with each of these two having a nearest neighbor to a fixed but otherwise arbitrary distance. This function describes special four-body configurations, but also contains contributions due to the so-called mutual nearest neighbor (two-body) and shared neighbor (three-body) configurations. The CPDF is introduced to improve a Helmholtz free energy method based on space partitions. We derive exact expressions of the CPDF and various associated quantities for randomly distributed, non-interacting points at Euclidean spaces of one, two and three dimensions. Results may be of interest in many diverse scientific fields, from fluid physics to social and biological sciences.
Rohrmann Rene D.
Zurbriggen Ernesto
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