Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...

This essay looks at the historical significance of four APS classic papers that are freely available online: Jolliffe N, Shannon JA, and Smith HW. The excretion of urine in the dog. III. The use of non-metabolized sugars in the measurement of the glomerular filtrate. Am J Physiol 100: 301-312, 1932 (http://ajplegacy.physiology.org/cgi/reprint/100/2/301). Shannon JA. The excretion of inulin by t...

By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...