Some applications of the Lambert W function to classical statistical mechanics

TL;DR

This paper explores the use of the Lambert W function in classical statistical mechanics, addressing problems like the Tonks gas and repulsive particle fluids through traditional and field theoretical approaches.

Contribution

It introduces new mathematical properties of the Lambert W function and applies it to classical statistical mechanics problems for the first time.

Findings

Derived new mathematical properties of the Lambert W function.

Applied Lambert W function to analyze the Tonks gas and repulsive fluids.

Bridged traditional and field theoretical methods in statistical mechanics.

Abstract

We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from the point of view of the standard theory of liquids and in the framework of a field theoretical description. Some new mathematical properties of the Lambert W function are obtained by passing.