Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics

TL;DR

This paper develops a mathematical framework for equilibrium thermodynamics, linking critical phenomena in Bose gases with phase transitions and introducing a tunnel generalization approach for complex thermodynamic behaviors.

Contribution

It introduces a novel mathematical theory connecting Bose gas degenerations with critical points and extends thermodynamics through tunnel generalization and quantization methods.

Findings

Degeneration points of Bose gases match critical points in thermodynamics.

Jumps in critical indices relate to tunnel generalization.

New critical points for pure gases and mixtures are identified.

Abstract

In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical points or real gases, whereas the jumps of critical indices and the Maxwell rule are related to the tunnel generalization of thermodynamics. Semiclassical methods are considered for the tunnel generalization of thermodynamics and also for the second and ultrasecond quantization (operators of creation and annihilation of pairs). To every pure gas there corresponds a new critical point of the limit negative pressure below which the liquid passes to a dispersed state (a foam). Relations for critical points of a homogeneous mixture of pure gases are given in dependence on the concentration of gases.