The workings of the maximum entropy principle in collective human behaviour

Abstract

We present an exhaustive study of the rank-distribution of city-population and population-dynamics of the 50 Spanish provinces (more than 8000 municipalities) in a time-window of 15 years (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010). We exhibit compelling evidence regarding how well the MaxEnt principle describes the equilibrium distributions. We show that the microscopic dynamics that governs population growth is the deciding factor that originates the observed macroscopic distributions. The connection between microscopic dynamics and macroscopic distributions is unravelled via MaxEnt.

Power-law and exponential rank distributions: A panoramic Gibbsian perspective

“…As noted in the introduction, entropy maximization is a known path to Zipf's law [25][26][27][28][29][30][31]. Also, it is known that entropy maximization on a log-size scale, subject to a given log-size mean, yields exponential log-size distributions -which, in turn, yield power-law size distributions [49].…”

“…And indeed, why do so many collaborative human endeavors result in quantities that are governed by Zipf's law? This intriguing question is a matter of vigorous scientific exploration, and familiar explanations include growth processes [10,18], preferential attachment [20][21][22], self-organized criticality [23,24], and entropy maximization [25][26][27][28][29][30][31]. In this paper we extend the entropymaximization approach, and present a comprehensive Gibbsian study of rank distributions-collections of positive-valued quantities that are ordered either decreasingly (as in the case of Zipf's law) or increasingly.…”

Zipf's law, power laws and maximum entropy

“…Specifically, a recent model of random group formation (RGF), see [8], attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy [9][10][11][12][13] applied to a particular choice of cost function [8]. (For recent related work largely in a demographic context see [14][15][16][17][18]. For related work in a fractal context implemented using an iterative framework see [19].…”

Maximum entropy principle analysis in network systems with short-time recordings

“…We again turn to the small network case of n = 2 nodes to demonstrate how to obtain a one-to-one mapping from the linear system described by Eq. (8). First, denote the vector J (2) as the vector containing all the effective interactions, with the index of each effective interaction, i.…”