A note on the entropy of repetitive sequences of symmetry group permutations

TL;DR

This paper observes that in signals with repeating symmetry group units, all entropy orders are equal, leading to improved metrics for measuring information content and similarity across data types.

Contribution

It introduces a novel insight that all entropy orders are equal in symmetric repeating sequences, enabling better metrics for information and similarity measurement.

Findings

All entropy orders are equal in symmetric repeating sequences.

New metrics improve comparison of information content across data.

Enhanced methods for analyzing text, signals, and genetic data.

Abstract

The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric for measuring the information content of higher order entropies in data such as text, signals, or genetics and another measure of similarity to compare the incremental information content across entropy orders when comparing data of different sizes and symbol sets or when comparing entire sequences.