Abstract
After establishing the formula of information, we turn to two cases: to the independent case and to the dependent case. If the characteristics of the particles (e.g., the energy) as random variables are independent, we come in the discrete case to the Boltzmann distribution, while in the continuous case we come to the Gibbs formula-irrespectively of whether the particles are distinguishable or not. Our effort is nimed at clarity of the ideas, not at their mathematical completeness.
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References
L. Boltzmann,Vorlesungen über Gastheorie, Berlin (1896).
S. N. Bose, “Plancks gesetz und lichtquanten hypothese,”Z. Phys.,26, 178–181 (1924).
S. Kullback and R. A. Leibler, “On Information and sufficiency,”Ann. Math. Statist.,22, 79–86 (1951).
I. N. Sanov, “On the probability of large deviations of random variables,” in:IMS and AMS Selected Translations in Mathematical Statistics and Probability, Vol. I (1961), pp. 213–214.
M. Planck, “Zur theorie des gesetzes der energieverteilung in normalspectrum,”Verhandl. Deutsch. Phys. Ges. (1900).
I. Vincze, “On an interpretation of a concept of information theory,”Matematikai Lapok,10, 255–266 (1959).
I. Vincze, “On certain distribution theorems of the statistical mechanics,”Math. Phys. Class, Hungar. Acad. Sci.,19, 117–130 (1969).
I. Vincze, “On the maximum probability principle in statistical physics,” in:Proceedings of European Meeting of Statisticians, Budapest, 1972, Coll. Math. Soc. János Bolzai,9 (1974).
I. Vincze and R. Tőrös,On the Planck-Bose-Einstein distribution, Probastat., Bratislava (1994).
F. Wilczek, “Anyons,”Scientific American, May, 24 (1991).
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Supported by the Hungarian National Foundation for Scientific Research (grant No. T 016384 and No. 4007-016237)
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part III.
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Vincze, I. Indistinguishability of particles or independence of the random variables?. J Math Sci 84, 1190–1196 (1997). https://doi.org/10.1007/BF02398432
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DOI: https://doi.org/10.1007/BF02398432