{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T01:25:45Z","timestamp":1771809945616,"version":"3.50.1"},"reference-count":76,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T00:00:00Z","timestamp":1603324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with \u201cfat\u201d tails, which can exactly be described with the q-Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.<\/jats:p>","DOI":"10.3390\/e22111194","type":"journal-article","created":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T20:51:00Z","timestamp":1603399860000},"page":"1194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing"],"prefix":"10.3390","volume":"22","author":[{"given":"Filippos","family":"Vallianatos","sequence":"first","affiliation":[{"name":"UNESCO Chair on Solid Earth Physics and Geohazards Risk Reduction, Institute of Physics of the Earth\u2019s Interior and Geohazards, Hellenic Mediterranean University Research Center, Crete, GR 73133 Chania, Greece"},{"name":"Department of Geophysics\u2013Geothermics, Faculty of Geology and Geoenvironment, National and Kapodistrian University of Athens, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0284-3867","authenticated-orcid":false,"given":"Georgios","family":"Michas","sequence":"additional","affiliation":[{"name":"UNESCO Chair on Solid Earth Physics and Geohazards Risk Reduction, Institute of Physics of the Earth\u2019s Interior and Geohazards, Hellenic Mediterranean University Research Center, Crete, GR 73133 Chania, Greece"},{"name":"Department of Geophysics\u2013Geothermics, Faculty of Geology and Geoenvironment, National and Kapodistrian University of Athens, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1111\/j.1365-246X.1995.tb07007.x","article-title":"Multifractal scaling properties of growing fault population","volume":"122","author":"Cowie","year":"1995","journal-title":"Geophys. 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