Diversity Assessment Based on a Higher Similarity-Higher Entropy Relation after Rejection of Gibbs Paradox

Abstract

The diversity of the symbols of the information source is calculated following the definition that entropy is the information loss and following a new entropy-symbol similarity relation after the rejection of the Gibbs paradox statement. Diversity in a range of 0 to 1, an index similar to Shannon's redundancy, decreases with the increase in the species similarities. A pairwise similarity formula has been defined and used to demonstrated that the diversity expression gives the expected diversity. The higher entropy-higher similarity relation leads to the higher information-higher diversity relation.