Toward a relative [formula omitted]-entropy

Abstract

We address the question and related controversy of the formulation of the q-entropy, and its relative entropy counterpart, for models described by continuous (non-discrete) sets of variables. We notice that an Lp normalized functional proposed by Lutwak–Yang–Zhang (LYZ), which is essentially a variation of a properly normalized relative Rényi entropy up to a logarithm, has extremal properties that make it an attractive candidate which can be used to construct such a relative q-entropy. We comment on the extremizing probability distributions of this LYZ functional, its relation to the escort distributions, a generalized Fisher information and the corresponding Cramér–Rao inequality. We point out potential physical implications of the LYZ entropic functional and of its extremal distributions.