摘要翻译：
为了描述和分析自组织临界(SOC)系统的动力学特性，提出了一种四状态连续时间马尔可夫模型。不同于通常用计算机模拟或数值实验的方法来解释SOC中的幂律，本文在此马尔可夫模型的基础上，利用E.T.Jayness的最大熵方法，导出了这些事件大小的幂律分布的数学证明。本文的Makov模型和幂律的数学证明为幂律分布的普适性提供了一个新的角度，并表明无标度性不仅存在于SOC系统中，而且存在于一类可以用所提出的Markov模型建模的动力系统中。
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英文标题：
《Markov Chain Hidden behind Power Law Mechanism of Self-organized
  Criticality》
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作者：
De Tao Mao and Yisheng Zhong
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最新提交年份：
2009
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  To describe and analyze the dynamics of Self-Organized Criticality (SOC) systems, a four-state continuous-time Markov model is proposed in this paper. Different to computer simulation or numeric experimental approaches commonly employed for explaining the power law in SOC, in this paper, based on this Markov model, using E.T.Jayness' Maximum Entropy method, we have derived a mathematical proof on the power law distribution for the size of these events. Both this Makov model and the mathematical proof on power law present a new angle on the universality of power law distributions, they also show that the scale free property exists not necessary only in SOC system, but in a class of dynamical systems which can be modelled by the proposed Markov model.
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PDF链接：
https://arxiv.org/pdf/709.2404