Thermal-equilibrium properties of one-dimensional gas with short-ranged repulsion

TL;DR

This paper derives an exact formula for the thermal-equilibrium spacing distribution in a one-dimensional gas with short-range repulsive potentials, specifically focusing on power-law interactions relevant to traffic modeling.

Contribution

It provides a novel exact analytical expression for the spacing distribution in a 1D gas with power-law repulsive potentials, advancing understanding of such systems.

Findings

Exact formula for spacing distribution derived

Focus on power-law potentials r^(-a) for a>0

Relevance to traffic research applications

Abstract

We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential depending on the distance r between the neighboring particles. We are focused on the power-law potentials r^(-a) for a>0, being motivated by the actual traffic research.