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Title: Power-law and exponential rank distributions: A panoramic Gibbsian perspective

Abstract

Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.

Authors:
Publication Date:
OSTI Identifier:
22451158
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 355; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTRIBUTION; ENTROPY; FREE ENTHALPY; STATISTICAL MODELS

Citation Formats

Eliazar, Iddo. Power-law and exponential rank distributions: A panoramic Gibbsian perspective. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.02.016.
Eliazar, Iddo. Power-law and exponential rank distributions: A panoramic Gibbsian perspective. United States. https://doi.org/10.1016/J.AOP.2015.02.016
Eliazar, Iddo. 2015. "Power-law and exponential rank distributions: A panoramic Gibbsian perspective". United States. https://doi.org/10.1016/J.AOP.2015.02.016.
@article{osti_22451158,
title = {Power-law and exponential rank distributions: A panoramic Gibbsian perspective},
author = {Eliazar, Iddo},
abstractNote = {Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.},
doi = {10.1016/J.AOP.2015.02.016},
url = {https://www.osti.gov/biblio/22451158}, journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 355,
place = {United States},
year = {Wed Apr 15 00:00:00 EDT 2015},
month = {Wed Apr 15 00:00:00 EDT 2015}
}