One-dimensional gas of hard needles

TL;DR

This paper investigates a one-dimensional gas of hard needles, using Monte Carlo simulations and analytical transfer matrix methods to study its thermodynamic properties, providing a comparison between computational and theoretical approaches.

Contribution

It introduces a formalism linking thermodynamic properties of hard potentials to contact probabilities, validated through Monte Carlo and analytical methods.

Findings

Monte Carlo calculations of pressure and elasticity coefficient

Comparison with analytical transfer matrix results

Validation of the formalism relating contact probabilities to thermodynamics

Abstract

We study a one dimensional gas of needle-like objects as a testing ground for a formalism that relates the thermodynamic properties of "hard" potentials to the probabilities for contacts between particles. Specifically, we use Monte Carlo methods to calculate the pressure and elasticity coefficient of the hard-needle gas as a function of its density. The results are then compared to the same quantities obtained analytically from a transfer matrix approach.