Keywordsgranger causality; transfer entropy; information theory; causal conditioning; conditional independence; information theory; information transfer; information storage; transfer entropy; information dynamics; cellular automata; complex systems; cardiovascular variability; conditional entropy; instantaneous causality; magnetoencephalography; time delay embedding; Liang-Kleeman information flow; causation; emergence; Frobenius-Perron operator; time series analysis; atmosphere-ocean science; El Niño; neuroscience; network dynamics; financial economics; transfer entropy; information transfer; entropy production; irreversibility; Kullback–Leibler divergence; thermodynamic equilibrium; Boltzmann’s principle; causal effect; transfer entropy; autoregressive process; Gaussian process; information transfer; direct Granger causality; multivariate time series; information measures; transfer entropy; joint entropy; coupling; interbank exposure matrix; risk contagion; transfer entropy; transfer entropy; dynamical systems; turbulence; cascades; shell models; Granger causality; information theory; transfer entropy; multivariate distributions; power-law distributions; financial markets; propagation of crises; transfer entropy; network inference; topological measures; transfer entropy; transfer entropy; information flow; statistical dependency; mutual information; Shannon entropy; information-theoretical quantities; Lorenz equations; entropy; transfer entropy; estimator; ensemble; trial; time series; entropy estimation; k nearest neighbors; transfer entropy; bias reduction; transfer entropy; causal relationships; entropy estimation; statistical dependency; nonlinear interactions; interacting subsystems; information-theory; Granger causality; mutual information; machine learning; data mining