The aim of this focus article is to present a comprehensive classification of the main entropic forms introduced in the last fifty years in the framework of statistical physics and information theory. Most of them can be grouped into three families, characterized by two-deformation parameters, introduced respectively by Sharma, Taneja, and Mittal (entropies of degree )), by Sharma and Mittal (entropies of order ), and by Hanel and Thurner (entropies of class ). Many entropic forms examined will be characterized systematically by means of important concepts such as their axiomatic foundations la Shannon-Khinchin and the consequent composability rule for statistically independent systems. Other critical aspects related to the Lesche stability of information measures and their consistency with the Shore-Johnson axioms will be briefly discussed on a general ground.

这篇焦点文章的目的是在统计物理学和信息论的框架内对过去五十年中引入的主要熵形式进行全面分类。它们中的大多数可以分为三个家族，以两个变形参数为特征，分别由 Sharma、Taneja 和 Mittal（度数的熵）、Sharma 和 Mittal（阶数的熵）、Hanel 和 Thurner（熵类）。审查会由重要的概念手段系统地表征许多熵形式，比如他们的公理基础LAShannon-Khinchin 和随之而来的统计独立系统的可组合性规则。与信息度量的 Lesche 稳定性及其与 Shore-Johnson 公理的一致性相关的其他关键方面将在一般情况下进行简要讨论。