118627 20230519145535.0 doi 10.3390/e23070908 sideral 126874 ART-2021-126874 eng Ishikawa A. Quasi-static variation of power-law and log-normal distributions of urban population 2021 Access copy available to the general public Unrestricted 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. © 2021 by the authors.Licensee MDPI, Basel Switzerland. info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.738 2021 PHYSICS, MULTIDISCIPLINARY 42 / 86 = 0.488 2021 Q2 T2 0.553 2021 Electrical and Electronic Engineering 2021 Q2 Physics and Astronomy (miscellaneous) 2021 Q2 Information Systems 2021 Q2 4.4 2021 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Fujimoto S. Ramos Gutiérrez, A. Universidad de Zaragoza (orcid)0000-0003-2618-1535 Mizuno T. 4000 415 Universidad de Zaragoza Dpto. Análisis Económico Área Fund. Análisis Económico 23, 7 (2021), 908 [16 pp] Entropy ENTROPY 1099-4300 2340444 http://zaguan.unizar.es/record/118627/files/texto_completo.pdf Versión publicada 2722871 http://zaguan.unizar.es/record/118627/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:118627 articulos driver 2023-05-18-15:35:33 ARTICLE