Physics of randomness and regularities for cities, languages, and their lifetimes and family trees

TL;DR

This paper models the evolution of cities and languages using multiplicative noise and fragmentation, revealing power law and log-normal distributions, and explores how regularities may emerge from randomness.

Contribution

It introduces a unified framework for understanding city and language evolution through stochastic processes, linking their size distributions and family dynamics.

Findings

Cities follow a Pareto-Zipf power law distribution.

Languages exhibit a slightly asymmetric log-normal distribution.

Lifetimes and family structures of cities and languages are characterized.

Abstract

Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size distribution of the cities and for that of the languages, respectively. The cities and the languages are treated differently (and as connected; for example, the languages split in terms of splitting the cities, etc.) and thus two distributions are obtained in the same computation at the same time. Evolutions of lifetimes and families for the cities and the languages are also studied. We suggest that the regularities may be evolving out of randomness, in terms of the relevant processes.