Equilibrium distributions in a thermodynamical traffic gas

We derive the exact formula for thermal-equilibrium spacing distribution of a one-dimensional particle gas with a repulsive potential V ( r) = r(-alpha)( alpha > 0) depending on the distance r between the neighbouring particles. The calculated distribution ( for alpha = 1) is successfully compared with the highway-traffic clearance distributions, which provides a detailed view of changes in the microscopical structure of a traffic sample depending on the traffic density. In addition to that, the observed correspondence is a strong support of studies applying the equilibrium statistical physics to traffic modelling.