Study Entropy of L-algebras

TL;DR

This paper revisits L-algebras and introduces the concept of entropy for L-algebras, providing methods to measure uncertainty and conditional entropy within these algebraic structures, along with propositions for dynamical systems.

Contribution

It introduces the notion of entropy for L-algebras and offers propositions for calculating entropy in dynamical systems involving these structures.

Findings

Defined entropy for L-algebras

Provided formulas for conditional entropy

Presented propositions for dynamical system entropy

Abstract

In this paper, the concept of L-algebra is revisited and after that, the article is prepared to deal with the notion of the entropy of an L-algebra. If a set has an L-algebraic structure, it is possible to calculate the degree of uncertainty for an event called partition. Sometimes one calculate the degree of uncertainty of an event given another event, which is actually called the conditional entropy. Some propositions are given to calculate the entropy of a dynamical system.