A gas of elongated objects; an analytical approach

TL;DR

This paper develops an analytical method to study thermodynamic properties of a one-dimensional gas of elongated objects, revealing how contact probabilities and rotational couplings influence these properties at different pressures.

Contribution

It introduces an approximation-based formalism that derives thermodynamic quantities analytically, independent of the noncentral potential at moderate pressures.

Findings

Quantities from the noncentral potential can be obtained from a central potential at moderate pressures.

The formalism reproduces key features of a gas of elongated objects.

Rotational couplings cause deviations in density-related quantities below a crossover pressure.

Abstract

We calculate a collective number of thermodynamic quantities in a one-dimensional gas of hard elongated objects (such as needles) whose centers mobile on a line. Our formalism uses an approximation for the probabilities of contact between the objects. We show that in moderate pressures the quantities extracted from the noncentral potential do not rely on its noncentrality, instead we can extract them analytically from a central potential. Our formalism reproduces the nontrivial features of a gas of elongated objects. Finally, we show below a crossover pressure $p_o$ the rotational couplings causes quantities proportional to inverse distance (such as density) are on average deviated from the inverse of average distance.