On the van der Waals gas, contact geometry and the Toda chain

TL;DR

This paper explores the connection between the van der Waals gas, contact geometry, and Toda chain symmetry, revealing underlying mathematical structures that unify these physical models.

Contribution

It uncovers a Toda chain symmetry in the van der Waals and ideal gases and investigates their links to contact geometry, providing new insights into their mathematical foundations.

Findings

Identification of Toda chain symmetry in the van der Waals gas

Connections established between contact geometry and thermodynamic models

Insights into the mathematical structure of ideal and van der Waals gases

Abstract

A Toda chain symmetry is shown to underlie the van der Waals gas and its close cousin, the ideal gas. Links to contact geometry are explored.