An overview of generalized entropic forms(a)

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 (alpha, beta)), by Sharma and Mittal (entropies of order (alpha, beta)), and by Hanel and Thurner (entropies of class (c, d)). Many entropic forms examined will be characterized systematically by means of important concepts such as their axiomatic foundations a 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. Copyright (C) 2021 EPLA

Automated summary

This focus article aims to present a comprehensive classification of main entropic forms introduced in the last fifty years in the fields of statistical physics and information theory. Three families of entropic forms are discussed, each characterized by different deformation parameters introduced by various researchers. Important concepts such as axiomatic foundations and composability rules for statistically independent systems are systematically applied to characterize many of these entropic forms. Other critical aspects related to information measures' stability and consistency with axioms are briefly discussed in a general context.