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A New Energy-Mass Equation: Review of Thermodynamics and Statistical Physics Analysis of Bose and Fermi Gases

Wen-Xiang Chen

Published Jun 20, 2024• 0 citations
Publisher

Abstract

Bose gases and Fermi gases represent two fundamental particle systems in statistical mechanics, governed by Bose-Einstein and Fermi-Dirac distributions, respectively. This paper provides a comprehensive analysis of the thermodynamic quantities, phase transitions, chemical potentials, and energy level relationships of these gases. The study utilizes Laurent series expansions and group theory analysis to explore the statistical properties and behavior of Bose and Fermi gases under various conditions. Additionally, the paper derives a new energy-mass equation based on metric and curvature \(R\).

DOI
10.33774/coe-2024-4lqlh

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Abstract This chapter presents the statistical description of quantum gases: bosons and fermions. The coarse-grained distribution function, measuring the average occupation of each quantum level is the fundamental object under study. In thermal equilibrium, gases obey the Bose—Einstein and Fermi—Dirac distributions. Out of equilibrium, a semiclassical description is adopted where the distribution functions evolve as particles and move among levels. For bosons, the presence of other particles in the final level enhances the transitions (stimulated emission), while for fermions they suppress the transition (Pauli exclusion principle). These effects are included semiclassically in the kinetic equation. It is shown that the quantum kinetic equation gives the correct evolution toward the equilibrium distributions. Phonons are worked out in detail, where the phonon–phonon and phonon–electron interactions affect the energy transport. Finally, lasers and the quark—gluon plasma are analysed in the context of the theory.