Abstract: This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.
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Balasis, G.; Donner, R.V.; Potirakis, S.M.; Runge, J.; Papadimitriou, C.; Daglis, I.A.; Eftaxias, K.; Kurths, J. Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System. Entropy 2013, 15, 4844-4888.
Balasis G, Donner RV, Potirakis SM, Runge J, Papadimitriou C, Daglis IA, Eftaxias K, Kurths J. Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System. Entropy. 2013; 15(11):4844-4888.
Balasis, Georgios; Donner, Reik V.; Potirakis, Stelios M.; Runge, Jakob; Papadimitriou, Constantinos; Daglis, Ioannis A.; Eftaxias, Konstantinos; Kurths, Jürgen. 2013. "Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System." Entropy 15, no. 11: 4844-4888.