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Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

1
Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, I. Metaxa & Vas. Pavlou St., GR-15236 Penteli, Greece
2
Research Domain IV—Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
3
Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, 07745 Jena, Germany
4
Department of Electronics Engineering, Technological Education Institute (TEI) of Piraeus, 250 Thivon and P. Ralli, GR-12244 Aigaleo, Athens, Greece
5
Department of Physics, Humboldt University, 12489 Berlin, Germany
6
Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Panepistimioupoli Zografou, 15784 Athens, Greece
7
Section of Solid State Physics, Department of Physics, University of Athens, Panepistimioupoli Zografou, 15784 Athens, Greece
8
Institute of Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, UK
*
Author to whom correspondence should be addressed.
The author's primary affiliation is 6.
Entropy 2013, 15(11), 4844-4888; https://doi.org/10.3390/e15114844
Received: 16 September 2013 / Revised: 22 October 2013 / Accepted: 22 October 2013 / Published: 7 November 2013
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
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. View Full-Text
Keywords: entropy measures; symbolic dynamics; non-extensive statistical mechanics; causality; Earth sciences entropy measures; symbolic dynamics; non-extensive statistical mechanics; causality; Earth sciences
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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.

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