Vallianatos Filippos, Michas Georgios
UNESCO Chair on Solid Earth Physics and Geohazards Risk Reduction, Institute of Physics of the Earth's Interior and Geohazards, Hellenic Mediterranean University Research Center, Crete, GR 73133 Chania, Greece.
Department of Geophysics-Geothermics, Faculty of Geology and Geoenvironment, National and Kapodistrian University of Athens, 15784 Athens, Greece.
Entropy (Basel). 2020 Oct 22;22(11):1194. doi: 10.3390/e22111194.
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 "fat" tails, which can exactly be described with the -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.
固体地球材料内部的破裂过程本质上是一个复杂的现象，以至于控制破裂起始和演化的基础物理学仍然难以捉摸。然而，通用标度关系似乎适用于破裂现象的集体特性。在本文中，我们基于非广延统计物理学（NESP）框架提出一种用于破裂的统计物理学方法。破裂现象通常呈现间歇性、多重分形性、长程相关性和极端波动，这些特性促使了NESP方法的产生。首先，我们简要回顾一下用于破裂和地震的NESP方法，然后分析北极海冰内的应力和应力方向时间序列。我们表明，此类时间序列呈现出大幅波动和具有“肥”尾的概率分布，这可以用在NESP框架中推导出来的非高斯分布精确描述。总体而言，NESP基于熵原理提供了一个一致的理论框架，用于推导破裂现象和地震的集体特性。
