The Distributions in Nature and Entropy Principle

The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is low, and the second one - when the ratio is high. The...

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Bibliographic Details
Published in:Turkish Economic Review 2016-12, Vol.3 (4), p.542
Main Author: KAFRI, Oded
Format: Article
Language:English
Online Access:Get full text
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Summary:The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is low, and the second one - when the ratio is high. The obtained long tail distribution yields correctly the empirical Zipf law, Pareto's 2080 rule and Benford's law. Therefore, it is concluded that the long tail and the "bell-like" distributions are outcomes of the tendency of statistical systems to maximize entropy.
ISSN:2149-0414
DOI:10.1453/ter.v3i4.1122