You might be interested in the complexity metric from shape dynamics involving the ratio of intra-cluster to inter-cluster distances [0], the magnitude metric f

You might be interested in the complexity metric from shape dynamics involving the ratio of intra-cluster to inter-cluster distances [0], the magnitude metric for maximal diversity [1], and haecceity [2] as repurposed for the meaning of entropy as specificity. [0] https://arxiv.org/pdf/2201.07979#subsection.5.1.2 https://arxiv.org/pdf/2201.07979#subsection.5.1.2 [1] https://case.edu/artsci/math/mwmeckes/publications.html https://case.edu/artsci/math/mwmeckes/publications.html [2] 'thisness' - in the sense that, the entropy quantifies the bits needed to pick some named option from more options