{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T18:50:22Z","timestamp":1778698222565,"version":"3.51.4"},"reference-count":236,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T00:00:00Z","timestamp":1383782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u00b4enyi 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.<\/jats:p>","DOI":"10.3390\/e15114844","type":"journal-article","created":{"date-parts":[[2013,11,7]],"date-time":"2013-11-07T15:28:06Z","timestamp":1383838086000},"page":"4844-4888","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":86,"title":["Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System"],"prefix":"10.3390","volume":"15","author":[{"given":"Georgios","family":"Balasis","sequence":"first","affiliation":[{"name":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, I. Metaxa & Vas. Pavlou St., GR-15236 Penteli, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reik","family":"Donner","sequence":"additional","affiliation":[{"name":"Research Domain IV\u2014Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany"},{"name":"Department of Biogeochemical Integration, Max Planck Institute for Biogeochemistry, 07745 Jena, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5928-4587","authenticated-orcid":false,"given":"Stelios","family":"Potirakis","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, Technological Education Institute (TEI) of Piraeus, 250 Thivon and P. Ralli, GR-12244 Aigaleo, Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakob","family":"Runge","sequence":"additional","affiliation":[{"name":"Research Domain IV\u2014Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany"},{"name":"Department of Physics, Humboldt University, 12489 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Constantinos","family":"Papadimitriou","sequence":"additional","affiliation":[{"name":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, I. Metaxa & Vas. Pavlou St., GR-15236 Penteli, Greece"},{"name":"Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Panepistimioupoli Zografou, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ioannis","family":"Daglis","sequence":"additional","affiliation":[{"name":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, I. Metaxa & Vas. Pavlou St., GR-15236 Penteli, Greece"},{"name":"Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Panepistimioupoli Zografou, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"Eftaxias","sequence":"additional","affiliation":[{"name":"Section of Solid State Physics, Department of Physics, University of Athens, Panepistimioupoli Zografou, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Kurths","sequence":"additional","affiliation":[{"name":"Research Domain IV\u2014Transdisciplinary Concepts & Methods, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany"},{"name":"Department of Physics, Humboldt University, 12489 Berlin, Germany"},{"name":"Institute of Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,7]]},"reference":[{"key":"ref_1","unstructured":"Tsallis, C. 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