Lima J A S, Deppman A
Departamento de Astronomia (IAG-USP), Universidade de São Paulo, 05508-090 São Paulo SP, Brasil.
Instituto de Física, Universidade de São Paulo, 05508-090 São Paulo, Brasil.
Phys Rev E. 2020 Apr;101(4-1):040102. doi: 10.1103/PhysRevE.101.040102.
Nonadditive Tsallis q-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticized by some authors based on the standard additive Boltzmann-Gibbs approach, thereby remaining a quite controversial subject. In order to clarify some polemical concepts, the distribution function for an ideal gas with a finite number of point particles and its q-index are analytically determined. The two-particle correlation function is also derived. The degree of correlation diminishes continuously with the growth of the number of particles. The ideal finite gas system is usually correlated, becomes less correlated when the number of particles grows, and is finally fully uncorrelated when the molecular chaos regime is reached. It is also advocated that both approaches can be confronted through a careful kinetic spectroscopic experiment. The analytical results derived here suggest that Tsallis q-statistics may play a physical role more fundamental than usually discussed in the literature.
非加性的Tsallis q统计量已成功应用于自然科学和其他知识分支中的大量系统。然而，基于标准的加性玻尔兹曼-吉布斯方法，一些作者对其基础提出了严厉批评，因此它仍然是一个颇具争议的主题。为了澄清一些有争议的概念，解析确定了具有有限数量点粒子的理想气体的分布函数及其q指数。还推导了两粒子关联函数。随着粒子数目的增加，关联程度持续降低。理想的有限气体系统通常是相关的，当粒子数增加时相关性减弱，最终在达到分子混沌状态时完全不相关。还主张可以通过仔细的动力学光谱实验来对比这两种方法。这里得出的解析结果表明，Tsallis q统计量可能发挥比文献中通常讨论的更为基本的物理作用。
