Multicanonical distribution and the origin of power laws

TL;DR

This paper introduces a multicanonical formalism to explain power-law distributions in complex systems by averaging Maxwell-Boltzmann distributions over fluctuating temperatures, resulting in hypergeometric function-based energy laws.

Contribution

It applies Bayesian analysis within a multicanonical framework to derive energy distributions with power-law tails in complex systems.

Findings

Derives energy distribution laws with power-law tails

Uses Bayesian analysis to determine temperature fluctuations

Connects hypergeometric functions to statistical equilibrium

Abstract

A multicanonical formalism is applied to the problem of statistical equilibrium in a complex system with a hierarchy of dynamical structures. At the small scales the system is in quasi-equilibrium and follows a Maxwell-Boltzmann distribution with a slowly fluctuating temperature. The probability distribution for the temperature is determined using Bayesian analysis and it is then used to average the Maxwell-Boltzmann distribution. The resulting energy distribution law is written in terms of generalized hypergeometric functions, which display power-law tails.