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Entropy 2013, 15(11), 4844-4888; doi:10.3390/e15114844
Review

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

1,* , 2,3
, 4
, 2,5
, 1,6
, 1,6,†
, 7
 and 2,5,8
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 The author's primary affiliation is 6.
* Author to whom correspondence should be addressed.
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)
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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.
Keywords: entropy measures; symbolic dynamics; non-extensive statistical mechanics; causality; Earth sciences entropy measures; symbolic dynamics; non-extensive statistical mechanics; causality; Earth sciences
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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