Statistical mechanics in the context of special relativity
Statistical mechanics in the context of special relativity
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DOI：
10.1103/physreve.66.056125
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发表时间：
2002-11-01
影响因子：
2.4
通讯作者：
Kaniadakis, G
中科院分区：
文献类型：
--
作者：
Kaniadakis, G
在参考文献[Physica A 296，405（2001）]中，从指数函数exp（{kappa}）（x）=（root 1 +kappa（2）x（2）+kappax）（1/kappa）的单参数变形开始，构造了随着变形参数kappa接近于零而还原为普通Boltzmann-Gibbs统计力学的统计力学。分布f=exp（{kappa}）（-beta E+betamu）在这个统计力学中得到的显示幂律尾部，并取决于非指定参数β，包含有关系统温度的所有信息。另一方面，熵的形式S-κ =integrald（3）p（c（κ）f（1+ κ）+c（-κ）f（1-κ）），在最大化之后产生分布f，并且当κ->0时简化为标准玻尔兹曼-香农熵S-0，包含系数c（κ），其表达式除了玻尔兹曼常数之外还涉及另一个未指定的参数α。在目前的努力中，我们表明，S-κ是唯一的现有的熵获得的连续变形的S-0和保持不变的基本属性，可加性，可拓性。S-kappa的这些性质允许明确地确定上述参数β和α的值。随后，我们解释了kappa引入的变形机制的起源，并表明这种变形在爱因斯坦狭义相对论中自然出现。此外，我们扩展的理论，以治疗统计系统的时间依赖性和相对论性的背景下。然后，我们表明，它是可能的，在一个自洽的计划内的狭义相对论的自由参数kappa值的结果取决于光速c和减少到零，因为c->无穷大，以这种方式恢复普通的统计力学和热力学。这里提出的统计力学，不包含自由参数，保持不变的数学和认识论结构的普通统计力学，是适合于描述一个非常大的类实验观察到的现象，在低，高能量物理和自然，经济和社会科学。最后，为了测试理论的正确性和可预测性，作为工作示例，我们考虑了宇宙射线光谱，其能量跨越13个十年，通量跨越33个十年，发现我们的预测与观测数据之间存在高质量的一致性。
In Ref. [Physica A 296, 405 (2001)], starting from the one parameter deformation of the exponential function exp({kappa})(x)=(root1+kappa(2)x(2) +kappax)(1/kappa), a statistical mechanics has been constructed which reduces to the ordinary Boltzmann-Gibbs statistical mechanics as the deformation parameter kappa approaches to zero. The distribution f=exp({kappa})(-beta E+betamu) obtained within this statistical mechanics shows a power law tail and depends on the nonspecified parameter beta, containing all the information about the temperature of the system. On the other hand, the entropic form S-kappa=integrald(3)p(c(kappa) f(1+kappa)+c(-kappa) f(1-kappa)), which after maximization produces the distribution f and reduces to the standard Boltzmann-Shannon entropy S-0 as kappa-->0, contains the coefficient c(kappa) whose expression involves, beside the Boltzmann constant, another nonspecified parameter alpha. In the present effort we show that S-kappa is the unique existing entropy obtained by a continuous deformation of S-0 and preserving unaltered its fundamental properties of concavity, additivity, and extensivity. These properties of S-kappa permit to determine unequivocally the values of the above mentioned parameters beta and alpha. Subsequently, we explain the origin of the deformation mechanism introduced by kappa and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter kappa which results to depend on the light speed c and reduces to zero as c-->infinity recovering in this way the ordinary statistical mechanics and thermodynamics. The statistical mechanics here presented, does not contain free parameters, preserves unaltered the mathematical and epistemological structure of the ordinary statistical mechanics and is suitable to describe a very large class of experimentally observed phenomena in low and high energy physics and in natural, economic, and social sciences. Finally, in order to test the correctness and predictability of the theory, as working example we consider the cosmic rays spectrum, which spans 13 decades in energy and 33 decades in flux, finding a high quality agreement between our predictions and observed data.