Toward a relative q-entropy

Nikolaos Kalogeropoulos

Physica A: Statistical Mechanics and its Applications, 2020, vol. 545, issue C

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.

Keywords: q-entropy; Tsallis entropy; Nonadditive entropy; Nonextensive thermostatistics; Complexity (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119318345

DOI: 10.1016/j.physa.2019.123270

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