Entropy (Jul 2021)

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

  • Atushi Ishikawa,
  • Shouji Fujimoto,
  • Arturo Ramos,
  • Takayuki Mizuno

DOI
https://doi.org/10.3390/e23070908
Journal volume & issue
Vol. 23, no. 7
p. 908

Abstract

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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.

Keywords