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Toward a relative q-entropy

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  • Kalogeropoulos, Nikolaos

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.

Suggested Citation

  • Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119318345
    DOI: 10.1016/j.physa.2019.123270
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    References listed on IDEAS

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    1. Creaco, Anthony J. & Kalogeropoulos, Nikolaos, 2019. "Irreversibility from staircases in symplectic embeddings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 497-509.
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