Additive deformations of statistical systems arise in various areas of physics. Classical central limit theory is then no longer applicable, even when standard independence assumptions are preserved. This paper investigates ways in which deformed algebraic operations lead to distinctive central limit theory. We establish some general central limit results that are applicable to a range of examples arising in nonextensive statistical mechanics, including the addition of momenta and velocities via Kaniadakis addition, and Tsallis addition. We also investigate extensions to random additive deformations, and find evidence (based on simulation studies) for a universal limit specific to each statistical system.

中文翻译：

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加性变形下的中心极限定理

统计系统的加性变形出现在物理学的各个领域。即使保留了标准的独立性假设，经典的中心极限理论也不再适用。本文研究了变形代数运算导致独特的中心极限理论的方式。我们建立了一些适用于非广延统计力学中出现的一系列例子的一般中心极限结果，包括通过 Kaniadakis 加法和 Tsallis 加法来增加动量和速度。我们还研究了随机加性变形的扩展，并找到了每个统计系统特有的通用限制的证据（基于模拟研究）。