An overview of generalized entropic forms^(a)

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