Related Experiment Video
Updated: May 18, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Conditional pair distributions in many-body systems: exact results for Poisson ensembles
René D Rohrmann1, Ernesto Zurbriggen
1Instituto de Ciencias Astronómicas, de la Tierra y del Espacio, UNSJ-CONICET, Av. España 1512 Sur, 5400 San Juan, Argentina. rohr@icate-conicet.gob.ar
Abstract:
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 within a certain distance of each 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, noninteracting 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.
Related Concept Videos
The Pauli Exclusion Principle
Poisson Probability Distribution
The...
Poisson's And Laplace's Equation
Equilibrium Conditions for a Particle
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
First Law: Particles in One-dimensional Equilibrium

