幂律尾统计分布的物理起源
Physical origin of the power-law tailed statistical distributions
摘要：
从描述非线性粒子系统动力学的BBGKY族出发，得到了相应的熵和定态分布函数。随后，通过使用洛伦兹变换，我们提出了指数和对数函数的相对论推广。相关的粒子分布和熵分别表示经典Maxwell-Boltzmann分布和Boltzmann熵的相对论性扩展，并且定义了在[Phys. Rev. E { \bf 66}，056125（2002）]和[Phys. Rev. E { \bf 72}，036108（2005）中提出的统计力学。本文的研究结果支持了这样一种观点，即实验观测到的等离子体物理中的幂律尾统计分布是由相对论微观粒子动力学强化的。
英文摘要：
Starting from the BBGKY hierarchy, describing the kinetics of nonlinear particle system, we obtain the relevant entropy and stationary distribution function. Subsequently, by employing the Lorentz transformations we propose the relativistic generalization of the exponential and logarithmic functions. The related particle distribution and entropy represents the relativistic extension of the classical Maxwell-Boltzmann distribution and of the Boltzmann entropy respectively and define the statistical mechanics presented in [Phys. Rev. E {\bf 66}, 056125 (2002)] and [Phys. Rev. E {\bf 72}, 036108 (2005). The achievements of the present effort, support the idea that the experimentally observed power law tailed statistical distributions in plasma physics, are enforced by the relativistic microscopic particle dynamics.
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