| Autor: |
Tai-Danae Bradley |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
Entropy, Vol 23, Iss 9, p 1195 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
1099-4300 |
| DOI: |
10.3390/e23091195 |
| Popis: |
We share a small connection between information theory, algebra, and topology—namely, a correspondence between Shannon entropy and derivations of the operad of topological simplices. We begin with a brief review of operads and their representations with topological simplices and the real line as the main example. We then give a general definition for a derivation of an operad in any category with values in an abelian bimodule over the operad. The main result is that Shannon entropy defines a derivation of the operad of topological simplices, and that for every derivation of this operad there exists a point at which it is given by a constant multiple of Shannon entropy. We show this is compatible with, and relies heavily on, a well-known characterization of entropy given by Faddeev in 1956 and a recent variation given by Leinster. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
|
Nepřihlášeným uživatelům se plný text nezobrazuje |
K zobrazení výsledku je třeba se přihlásit.
|
