Zipf's law from a Fisher variational-principle

TL;DR

This paper demonstrates that Zipf's law can be derived as a variational solution using Fisher information principles, explaining its universality across different datasets like citation distributions.

Contribution

It introduces a Fisher variational principle approach to derive Zipf's law, linking information theory with observed rank distributions.

Findings

Citation counts in top physics journals follow Zipf's law

The variational approach explains the universality of Zipf's law

Fisher information and scale-invariance underpin the distribution

Abstract

Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example we show that the number of citations found in the most referenced physics journals follows this law.