About the Entropy of a Natural Number and a Type of the Entropy of an Ideal-Reference-Cited by-同舟云学术

About the Entropy of a Natural Number and a Type of the Entropy of an Ideal

Published:2023-03-24 Issue:4 Volume:25 Page:554
ISSN:1099-4300
Container-title:Entropy
language:en
Short-container-title:Entropy

Author:

Minculete Nicuşor¹^ORCID,Savin Diana¹

Affiliation:

1. Faculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Street 50, 500091 Braşov, Romania

Abstract

In this article, we find some properties of certain types of entropies of a natural number. We are studying a way of measuring the “disorder” of the divisors of a natural number. We compare two of the entropies H and H¯ defined for a natural number. An useful property of the Shannon entropy is the additivity, HS(pq)=HS(p)+HS(q), where pq denotes tensor product, so we focus on its study in the case of numbers and ideals. We mention that only one of the two entropy functions discussed in this paper satisfies additivity, whereas the other does not. In addition, regarding the entropy H of a natural number, we generalize this notion for ideals, and we find some of its properties.

Funder

Transilvania University of Braşov

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/1099-4300/25/4/554/pdf

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