Simple geometrical interpretation of the linear character for the Zeno-line and the rectilinear diameter

TL;DR

This paper presents a unified geometrical interpretation explaining the linear relationships of the Zeno-line and rectilinear diameter in molecular fluids, linking empirical observations to a projective isomorphism with the lattice gas model.

Contribution

It introduces a novel geometrical framework connecting empirical linearities in fluids to the Ising model via projective isomorphism.

Findings

Zeno-line and rectilinear diameter are linked through projective geometry.

Empirical relations in fluids can be derived from lattice gas model properties.

The approach unifies different empirical linearities under a common geometrical interpretation.

Abstract

The unified geometrical interpretation of the linear character of the Zeno-line (unit compressibility line Z=1) and the rectilinear diameter is proposed. We show that recent findings about the properties of the Zeno-line and striking correlation with the rectilinear diameter line as well as other empirical relations can be naturally considered as the consequences of the projective isomorphism between the real molecular fluids and the lattice gas (Ising) model.