A New Perspective of Entropy

Tai-Danae Bradley
PhD, Mathematics, CUNY Graduate Center
Research Mathematician at Sandbox@Alphabet
Visiting Research Professor of Mathematics at The Master’s University

Published: Spring 2022, Vol. 1, Issue 1, pp. 35–65
DOI: doi.org/10.55409/math3ma2022-112

Abstract: This article describes a new connection between two seemingly disparate topics in science, namely entropy and higher mathematics. It does not assume prior knowledge of either subject and be- gins with a brief introduction to information theory and a concept known as Shannon entropy, which we simply refer to as entropy. We then survey the vast landscape of higher mathematics, giving spe- cial attention to advanced analogues of high-school algebra and geometry known as abstract algebra and topology, respectively. Our goal is then to show that entropy, abstract algebra, and topology are inextricably linked through a version of a well-known formula from calculus known as the Leibniz rule. This result is given in the author’s recent work in [Bra21], and this present article is intended to give an overview of the ideas by gently introducing them from the ground up.

[Bra21] Tai-Danae Bradley. Entropy as a topological operad derivation. Entropy, 23(9), 2021.