Renyi entropy and power-law distributions in natural and human sciences

Abstract

Traditional Boltzmann‐Gibbs statistic thermodynamics does not provide power-law distributions characterizing complex self-organizing systems [1]. In this work, we propose using a more general approach involving Renyi entropy that makes it possible to adequately describe complex self-organizing systems. Power-law distributions are observed in various fields of natural sciences and in the social and economic activity of mankind [2] and are known as Zipf’s law in linguistics; the Pareto law in economics and sociology of science; the Gutenberg‐Richter law in geophysics; and power-law distributions for critical phenomena, for the intensity of avalanches in a granulated medium, for fragment masses upon impact fragmentation, for the energy spectrum of particles in the atmospheric cascades of cosmic rays, for users of Web sites, etc. On the other hand, the maximum of the Gibbs‐Shannon entropy