Molecular Diversity Assessment: Logarithmic Relations of Information and Species Diversity and Logarithmic Relations of Entropy and Indistinguishability after Rejection of Gibbs Paradox of Entropy of Mixing

It is postulated that the degradation of species diversity results in information loss or entropy increase. To define the molecular diversity of either a single mixture of different compounds and a combinatorial compound library or a collection of pure compounds, we treat them all as molecular assemblages for information registration and consider only the molecular similarity and chemical species numbers of the individual molecules. The entropy of a molecular assemblage is correlated to the chemical species similarity via the von Neumann-Shannon relation and related to the so-defined apparent species indistinguishability number (σa) via a logarithmic relation. Information and the apparent species number (Ma) also have a logarithmic relation. Ma is equal to or less than the designated species number M. The diversity index (D) is defined as the ratio of the logarithms of the apparent chemical species number and the designated species number (D=lnMa/lnM). D has a value between 0 and 1 and decreases with the increase in similarity among the species. The decrease in the evenness of the species abundance also results in a decrease in diversity D. Molecular diversity of a combinatorial compound library is determined by the available number of component variants and their similarity. Clearly these concepts and formulae can also be applied to calculate biodiversity.