An Optimization-Based Generative Model of Power Laws Using a New Information Theory Based Metric

TL;DR

This paper introduces an optimization-based model for power law distributions using a new information theory inspired metric, linking entropy, energy, and distribution tail behavior.

Contribution

It presents a novel optimization framework with a mathematically derived function that explains power law distributions, integrating concepts of entropy and energy.

Findings

The model successfully reproduces power law distributions.

The derived function aligns with entropy and energy concepts.

Results demonstrate the effectiveness of the optimization approach.

Abstract

In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this function are analyzed. The derived function shows some similarity to the entropy function in representing order and randomness; however, it also represents the energy, where the optimization process is seeking to maximize the number of elements at the tail of the distribution constrained by the total amount of the energy. The results show a matching between the output of the optimization process and the power law distribution.