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Nongeneralizability of Tsallis Entropy by means of Kolmogorov-Nagumo averages under pseudo-additivity

Ambedkar Dukkipati·M. Narsimha Murty·Shalabh Bhatnagar
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Abstract

As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity is a characteristic property of Tsallis entropy. Renyi generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint.In this paper we show that there exists no generalization for Tsallis entropy, by means of Kolmogorov-Nagumo averages, which preserves the pseudo-additivity.

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Ambedkar Dukkipati, M. Narsimha Murty, Shalabh Bhatnagar. 2005-05-30. Nongeneralizability of Tsallis Entropy by means of Kolmogorov-Nagumo averages under pseudo-additivity. https://arxiv.org/abs/math-ph/0505078

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