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Bulletin of University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca Veterinary Medicine

Bose-Einstein and Fermi-Dirac Distributions and Their Use in Biological Sciences

Monica G. Hăşmăşanu, Sorana Daniela Bolboaca, Lorentz Jäntschi

Published May 27, 2014• 2 citations
Publisher

Abstract

The aim of this paper was to review and summarize the usefulness of Bose-Einstein and Fermi-Dirac distributions in biological sciences. Starting with the introductory presentation of these distributions, the paper presents their rationale, formulas and applications. Furthermore, the increase interest of applying Bose-Einstein and Fermi-Dirac statistics in nowadays life science researches has also been highlighted.

DOI
10.15835/buasvmcn-vm:71:1:10141

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The aim of this paper was to review and summarize the usefulness of Bose-Einstein and Fermi-Dirac distributions in biological sciences. Starting with the introductory presentation of these distributions, the paper presents their rationale, formulas and applications. Furthermore, the increase interest of applying Bose-Einstein and Fermi-Dirac statistics in nowadays life science researches has also been highlighted.
Some fundamental changes have been introduced into statistical theory since the publication of a paper by Bose in 1924. The characteristic features of the new statistics, including that of Bose and Einstein, and the later one of Fermi and Dirac, are pointed out in this lecture and compared with the classical statistics. A number of recent applications of the new ideas are described, including the work of Thomas and Fermi on the distribution of electrons in atoms, and the work of Sommerfeld and others on the electron theory of metals. An account is also given of some recent results obtained by the author and H. J. Woods on the distribution of electrons in a metal.
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 RRR.
We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution function interpolates continuously between the Fermi-Dirac and the Bose-Einstein limits. We present an explicit solution of the transcendental equation for the didtribution function in a general case, as well as determine the thermodynamic properties in both low- and high-temperature limits.