Thermodynamics of Van der Waals Fluids with quantum statistics

TL;DR

This paper extends the classical van der Waals theory to quantum systems, deriving general thermodynamic relations and applying them to nuclear matter and relativistic boson gases, revealing quantum effects like Fermi and Bose-Einstein phenomena.

Contribution

It provides a unifying quantum generalization of van der Waals thermodynamics and explores quantum phase transitions in nuclear and bosonic gases.

Findings

Quantum van der Waals fluid models nuclear liquid-gas critical point.

Bose-Einstein condensation leads to spatially separated two-phase structure.

General thermodynamic relations for quantum gases are derived.

Abstract

We consider thermodynamics of the van der Waals fluid of quantum systems. We derive general relations of thermodynamic functions and parameters of any ideal gas and the corresponding van der Waals fluid. This provides unambiguous generalization of the classical van der Waals theory to quantum statistical systems. As an example, we apply the van der Waals fluid with fermi statistics to characterize the liquid-gas critical point in nuclear matter. We also introduce the Bose-Einstein condensation in the relativistic van der Waals boson gas, and argue, that it exhibits two-phase structure separated in space.