Variational principle for the Pareto power law
Abstract
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems. The derivation only uses a variational principle based on the Boltzmann entropy, without assumptions outside the framework of canonical equilibrium statistical mechanics. Two examples are discussed, free diffusion on a complex network and a kinetic model of wealth exchange. The mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system.
Keywords
Cite
@article{arxiv.cond-mat/0605325,
title = {Variational principle for the Pareto power law},
author = {Anirban Chakraborti and Marco Patriarca},
journal= {arXiv preprint arXiv:cond-mat/0605325},
year = {2018}
}
Comments
Revised version, 4 pages and 1 figure