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 criticised 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. It is shown that the finite gas is usually correlated, becomes less correlated whether the number of particles grows, and, finally, fully uncorrelated when the molecular chaos regime is reached. It is also advocated that both approaches can be confronted through a careful kinetic experiment. These analytical results describing one of the simplest systems in nature suggest that Tsallis q-statistics may have a more fundamental role than the standard statistical description.

中文翻译：

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Tsallis满足有限的理想气体及其热力学极限的Boltzmann：q指数

非加性Tsallis q统计已成功应用于自然科学和其他知识分支的众多系统。然而，基于标准加性玻尔兹曼-吉布斯方法的一些作者已经严重批评了它的基础，因此仍然是一个颇有争议的话题。为了阐明一些矛盾的概念，分析确定了具有有限数量的点粒子的理想气体的分布函数及其q指数。还推导了两个粒子的相关函数。结果表明，有限气体通常是相关的，而无论粒子数量是否增长，其相关性都会降低，最后，当达到分子混沌状态时，它们将完全不相关。还主张可以通过仔细的动力学实验来面对这两种方法。