Zeno-line, Binodal, T-{\rho} Diagram and Clusters as a new Bose-Condensate Bases on New Global Distributions in Number Theory

TL;DR

This paper establishes a link between thermodynamic diagrams and number theory, introducing a new Bose condensate model for classical gases that leverages global distributions to reduce fractal dimensions while conserving particle count.

Contribution

It introduces a novel correspondence principle connecting thermodynamic diagrams with number theory distributions, and constructs a new Bose condensate model for classical gases.

Findings

Established a correspondence between T-ρ diagram, Zeno line, and binodal.

Developed a new Bose-Einstein type distribution for classical gases.

Demonstrated reduction of fractal dimension while preserving particle number.

Abstract

We present the correspondence principle between the T-{\rho} diagram, the Zeno line and the binodal for a given interaction potential of Lennard-Jones type. We use this correspondence further to construct a distribution of the Bose-Einstein type for a classical gas with the help of the new notion of Bose condensate, making it possible to decrease fractal dimension while simultaneously preserving the number of particles. In so doing, we use new global distributions in number theory.