Detecting causality in coupled systems using recurrence analysis and maximum entropy principle

The study of coupled dynamical systems is fundamental for understanding complex real-world phenomena. Such complexity arises from the interactions among a large number of components, or nodes, whose collective behavior cannot be inferred from the dynamics of individual elements alone. Even when each node is well characterized, the global dynamics often exhibit emergent patterns that are not a simple superposition of their parts. Consequently, uncovering the interactions between nodes is essential for explaining the behavior of complex systems. This task becomes particularly challenging when only observational signals are available, and even more so when the directionality of interactions (causality) must be determined. In this work, we propose a novel approach for detecting causal interactions based on the maximum entropy principle applied to recurrence microstates (RM). The method enables the estimation of conditional information transfer between coupled systems while reducing the parametric dependence inherent in the Recurrence Measure of Conditional Dependence (RMCD), thereby enhancing its robustness and effectiveness. We demonstrate the performance of the proposed framework across a range of systems with increasing complexity, including stochastic processes (autoregressive moving average, ARMA), discrete chaotic systems (coupled logistic and Rulkov maps), and continuous chaotic systems (Lorenz system). Finally, we apply the method to real-world data from the COVID-19 pandemic in the three most populous Brazilian states, spanning March 2020 to December 2022. In this context, we investigate the causal influence of fluctuations in reported case numbers on subsequent deaths, providing empirical validation of the method in a realistic and socially relevant scenario.