Information theory in non-linear dynamics and causality: State-space partition or ordinal patterns?

Information theory provides powerful tools for the analysis of time series generated by interacting nonlinear systems. Coupling and causal relationships can be identified and characterized in terms of information transfer, while the complexity of the underlying dynamics can be quantified through rates of entropy production. The practical evaluation of information-theoretic measures, however, requires the estimation of multidimensional probability distributions from experimental time series, which is often challenging. In this work, we analyze and discuss the applicability of replacing state-space partitioning with ordinal patterns encoding continuous data into discrete symbolic representations.