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Article

Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population

by 1,*,†, 1,†, 2,† and 3,4,5,†
1
Department of Economic Informatics, Kanazawa Gakuin University, Kanazawa 920-1392, Japan
2
Department of Economic Analysis, Universidad de Zaragoza, 50005 Zaragoza, Spain
3
National Institute of Informatics, Tokyo 101-8430, Japan
4
The Graduate University for Advanced Studies [SOKENDAI], Kanagawa 240-0193, Japan
5
Center for Advanced Research in Finance, The University of Tokyo, Tokyo 113-0033, Japan
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Dimitri Volchenkov
Entropy 2021, 23(7), 908; https://doi.org/10.3390/e23070908
Received: 11 June 2021 / Revised: 5 July 2021 / Accepted: 14 July 2021 / Published: 17 July 2021
(This article belongs to the Special Issue Mathematical Analysis of Urban Spatial Networks)
We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry. View Full-Text
Keywords: urban population; power law; log-normal distribution; Gibrat’s law; non-gibrat property; quasi-time-reversal symmetry urban population; power law; log-normal distribution; Gibrat’s law; non-gibrat property; quasi-time-reversal symmetry
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MDPI and ACS Style

Ishikawa, A.; Fujimoto, S.; Ramos, A.; Mizuno, T. Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population. Entropy 2021, 23, 908. https://doi.org/10.3390/e23070908

AMA Style

Ishikawa A, Fujimoto S, Ramos A, Mizuno T. Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population. Entropy. 2021; 23(7):908. https://doi.org/10.3390/e23070908

Chicago/Turabian Style

Ishikawa, Atushi, Shouji Fujimoto, Arturo Ramos, and Takayuki Mizuno. 2021. "Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population" Entropy 23, no. 7: 908. https://doi.org/10.3390/e23070908

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