Nongeneralizability of Tsallis Entropy by means of Kolmogorov-Nagumo averages under pseudo-additivity
نویسندگان
چکیده
As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity of the form x+qy = x+y+(1−q)xy is a characteristic property of Tsallis entropy. Rényi in [1] 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.
منابع مشابه
Uniqueness of Nonextensive entropy under Renyi's Recipe
By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...
متن کاملThermostatistics based on Kolmogorov–Nagumo averages: unifying framework for extensive and nonextensive generalizations
We show that extensive thermostatistics based on Rényi entropy and Kolmogorov–Nagumo averages can be expressed in terms of Tsallis nonextensive thermostatistics. We use this correspondence to generalize thermostatistics to a large class of Kolmogorov–Nagumo means and suitably adapted definitions of entropy. As an application, we reanalyze linguistic data discussed in a paper by Montemurro. 20...
متن کاملOn Generalized Measures of Information with Maximum and Minimum Entropy Prescriptions
Kullback-Leibler relative-entropy or KL-entropy of P with respect to R defined as ∫ X ln dP dR dP , where P and R are probability measures on a measurable space (X,M), plays a basic role in the definitions of classical information measures. It overcomes a shortcoming of Shannon entropy – discrete case definition of which cannot be extended to nondiscrete case naturally. Further, entropy and oth...
متن کاملGeneralized thermostatistics and Kolmogorov-Nagumo averages
We introduce a generalized thermostatistics based on Kolmogorov-Nagumo averages and appropriately selected information measures. The formalism includes Tsallis non-extensive thermostatistics, but also extensive thermostatistics based on Rényi entropy. The Curie-Weiss model is discussed as an example.
متن کاملOn the Uniqueness Theorem for Pseudo-Additive Entropies
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-...
متن کامل