Quasi-set-theoretical foundations of statistical mechanics: a research program

Details Quasi-set-theoretical foundations of statistical mechanics: a research program Quasi-set-theoretical foundations of statistical mechanics: a research program

1999-06-12

arxiv.org/abs/quant-ph/9906038v1

Found.Phys. 30 (2000) 101-120

Physics

Quantum Physics

LaTeX, 19 pages, 3 figures

Scientific paper

Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell-Boltzmann statistics, it is not necessary to assume that the particles are distinguishable. In other words, Maxwell-Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to provide the mathematical grounds of a quasi-set-theoretical framework for statistical mechanics.

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