Entropy (Mar 2023)

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

  • Nicuşor Minculete,
  • Diana Savin

DOI
https://doi.org/10.3390/e25040554
Journal volume & issue
Vol. 25, no. 4
p. 554

Abstract

Read online

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.

Keywords