Abstract
The long history of ergodic and quasi-ergodic hypotheses provides the best example of the attempt to supply non-probabilistic justifications for the use of statistical mechanics in describing mechanical systems. In this paper we reverse the terms of the problem. We aim to show that accepting a probabilistic foundation of elementary particle statistics dispenses with the need to resort to ambiguous non-probabilistic notions like that of (in)distinguishability. In the quantum case, starting from suitable probability conditions, it is possible to deduce elementary particle statistics in a unified way. Following our approach Maxwell-Boltzmann statistics can also be deduced, and this deduction clarifies its status.Thus our primary aim in this paper is to give a mathematically rigorous deduction of the probability of a state with given energy for a perfect gas in statistical equilibrium; that is, a deduction of the equilibrium distribution for a perfect gas. A crucial step in this deduction is the statement of a unified statistical theory based on clearly formulated probability conditions from which the particle statistics follows. We believe that such a deduction represents an important improvement in elementary particle statistics, and a step towards a probabilistic foundation of statistical mechanics.In this Part I we first present some history: we recall some results of Boltzmann and Brillouin that go in the direction we will follow. Then we present a number of probability results we shall use in Part II. Finally, we state a notion of entropy referring to probability distributions, and give a natural solution to Gibbs' paradox.
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DOI 10.1016/s1355-2198(97)00014-2
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References found in this work BETA

On the Impossible Pilot Wave.J. S. Bell - 1982 - Foundations of Physics 12 (10):989-999.
The Relevance Quotient.Domenico Costantani - 1979 - Erkenntnis 14 (2):149 - 157.

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Citations of this work BETA

A Probabilistic Foundation of Elementary Particle Statistics. Part II.Domenico Costantini & Ubaldo Garibaldi - 1998 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 29 (1):37-59.
Boltzmann and the Heuristics of Representation in Statistical Mechanics.Cássio C. Laranjeiras, Jojomar Lucena & José R. N. Chiappin - 2020 - Transversal: International Journal for the Historiography of Science 8:72.
A Probabilistic Foundation of Elementary Particle Statistics. Part II.Domenico Costantini & Ubaldo Garibaldi - 1998 - Studies in History and Philosophy of Modern Physics 29 (1):37-59.

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