These kinds of non-linear measures are pretty interesting. I have a book sitting on a shelf by Kantz and Schreiber called _Nonlinear Time Series Analysis_ (2nd edition). I haven't really looked at it. But almost all of conventional statistics, frequentist, information theoretic, or Bayesian, is linear. And tucked in amongst the new algorithms of machine learning are nonlinear approaches which we don't entirely understand and are pretty powerful, notions like _boosting_, for which no one has done a thorough theoretical analysis, although there have been promising approaches. Same for _random forests_ and other tree-based methods. And then there are hybrids or extensions ... I bet somewhere there there is lurking a quasi-tree-based approach which uses continuous measures across supports akin to Bayesian membership scores instead of ensembles of discrete splits. Don't know how that goes, but it would be an interesting thing to develop and explore.