Remarks on “Comments on ‘On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-non-extensive statistics with non-Tsallisian entropy’ ” [Physica A 466 (2017) 160]

2017

Physics Letters A

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The paper introduces nonadditivity parameter transformation group induced by Tsallis entropy. We discuss simple physical applications of a system in the contact with finite heat bath or with temperature fluctuations. With help of the transformation, it is possible to introduce generalized distributive rule in q-deformed algebra. We focus on MaxEnt distributions of Tsallis entropy with rescaled nonadditivity parameter under escort energy constraints. We show that each group element corresponds to one class of q-deformed distributions. Finally, we briefly discuss the application of the transformation to Jizba-Arimitsu Hybrid entropy and its connection to Average Hybrid entropy

“…Refs. [14,52,53,25]. Similarly to Tsallis entropy, it follows q-deformed additivity rule for independent events.…”

Section: Maxent Distributions Of Tsallis Entropy With Rescaled Nonadd...mentioning

confidence: 82%

“…6. Note on Jizba-Arimitsu Hybrid entropyJizba-Arimitsu Hybrid entropy was defined as the overlap between Tsallis entropy and Rényi entropy[9] and its properties have been recently discussed in Refs [14,52,53,25]…”

mentioning

confidence: 99%

Rescaling the nonadditivity parameter in Tsallis thermostatistics

2017

Physics Letters A

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“…It is purpose of this paper to focus on the axiomatic underpinning of entropies with a special emphasize on the axiomatics of the so-called q-additive entropies. We shall show, by extending our previous argument [15], that commonly used axioms for q-additive entropies are prone to have multiplicity of distinct solutions with the culprit residing in the way how conditional entropies are handled. Since the existence of different solutions is intimately related to Darótzy's mapping theorem and Kolmogorov-Nagumo's quasi-linear means, we study thus generated class of entropic functionals that all satisfy the same q-additive entropic chain rule.…”

Section: Introductionmentioning

confidence: 65%

“…Here R(q) kl is the correct would-be joint escort distribution. Note that R(q) kl is not the escort of r kl and R(q) kl = R(q) kl iff events are independent [15].…”

Section: Two Simple Theoremsmentioning

confidence: 99%

See 1 more Smart Citation

On the Uniqueness Theorem for Pseudo-Additive Entropies

Jizba

2017

Entropy

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Abstract:The aim of this paper is to show that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. By using the concept of Kolmogorov-Nagumo quasi-linear means, we prove this with the help of Darótzy's mapping theorem. Our point is further illustrated with a number of explicit examples. Other salient issues, such as connections of conditional entropies with the de Finetti-Kolmogorov theorem for escort distributions and with Landsberg's classification of non-extensive thermodynamic systems are also briefly discussed.

On statistical properties of Jizba–Arimitsu hybrid entropy

Çankaya

Physica A: Statistical Mechanics and its Applications

2017

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Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of Rényi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are completely different from the former two entropies. In this paper, we demonstrate the statistical properties of hybrid entropy, including the definition of hybrid entropy for continuous distributions, its relation to discrete entropy and calculation of hybrid entropy for some well-known distributions. Additionally, definition of hybrid divergence and its connection to Fisher metric is also discussed. Interestingly, the main properties of continuous hybrid entropy and hybrid divergence are completely different from measures based on Rényi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Rényi entropy