  The similarity of local atomic environments is an important concept in many
machine-learning techniques which find applications in computational chemistry
and material science. Here, we present and discuss a connection between the
information entropy and the similarity matrix of a molecule. The resulting
entropy can be used as a measure of the complexity of a molecule. Exemplarily,
we introduce and evaluate two specific choices for defining the similarity: one
is based on a SMILES representation of local substructures and the other is
based on the SOAP kernel. By tuning the sensitivity of the latter, we can
achieve a good agreement between the respective entropies. Finally, we consider
the entropy of two molecules in a mixture. The gain of entropy due to the
mixing can be used as a similarity measure of the molecules. We compare this
measure to the average and the best-match kernel. The results indicate a
connection between the different approaches and demonstrate the usefulness and
broad applicability of the similarity-based entropy approach.
