Variational Principle underlying Scale Invariant Social Systems

TL;DR

This paper extends the MaxEnt principle by incorporating dynamical information, enabling it to model scale-invariant social phenomena like city populations with a unifying thermodynamic-like framework.

Contribution

It introduces a generalized MaxEnt approach that accounts for dynamical information, explaining scale-invariant social distributions beyond exponential forms.

Findings

MaxEnt with dynamical info models city-population distributions.

Numerical experiments confirm the generalized MaxEnt predictions.

Comparison with empirical data supports the approach.

Abstract

MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the incorporation, into the variational process, of suitable dynamical information. As a consequence, we are able to formulate a somewhat generalized Shannonian Maximum Entropy approach which provides a unifying "thermodynamic-like" explanation for the scale-invariant phenomena observed in social contexts, as city-population distributions. We confirm the MaxEnt predictions by means of numerical experiments with random walkers, and compare them with some empirical data.