Related papers: Comments on paper by B.Lesche (Phys. Rev. E {\bf 7…
It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.
Bashkirov's comments (cond-mat/0410667) on the paper [S. Abe, Phys. Rev. E 66, 046134 (2002)] are all refuted. In addition, it is discussed that the Renyi entropy is irrelevant to generalization of Boltzmann-Gibbs statistical mechanics for…
It is shown that the R\'enyi and Tsallis entropies and the q-expectation values, are continuous and stable if $q>1$ and are not continuous and instable for uniform finite distributions if $q<1$.
We prove that the inequality used recently by Wilk and W{\l}odarczyk [Phys. Rev. A {\bf 79}, 062108 (2009)] to find a better lower bound in the uncertainty relations for the R\'enyi entropies is invalid. Thus, the problem of improving the…
The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the…
Oikonomou [Physica A 386 (2007) 119] has published a calculation which purports to show that the Tsallis and Renyi entropies can be obtained from the generalized multinomial coefficients. In this paper, we prove that the method of…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
In this paper, we give a new method for proving the Lesche stability of several functionals(Incomplete entropy, Tsallis entropy, \kappa - entropy, Quantum-Group entropy). We prove also that the Incomplete q - expectation value and Renyi…
The equilibrium distributions of probabilities providing maximality of Renyi and Tsallis entropies are rederived. New S-forms of them are found which are normalised with corresponding entropies in contrast to the usual Z-forms normalised…
We provide a unifying axiomatics for Renyi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszar's measure of directed divergence known from communication theory.
Despite recent claims we argue that Renyi's entropy is an observable quantity. It is shown that, contrary to popular belief, the reported domain of instability for Renyi entropies has zero measure (Bhattacharyya measure). In addition, we…
Here we explain how C. Tsallis' reply (Entropy 2021, 23(5), 630) fails to respond to points raised in (Entropy 2020, 22(10), 1110) and introduces further inconsistencies on the origin of black hole entropy. In his reply, Tsallis argues that…
The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they…
We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw [Phys. Lett. A {\bf 198} (1995) 119] has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient…
The R\'enyi and Tsallis entropies are discussed as possible alternatives to the Bekenstein-Hawking area-law entropy. It is pointed out how replacing the entropy notion, but not the Hawking temperature and the thermodynamical energy may…
The equivalence between non-extensive C. Tsallis entropy and the extensive entropy introduced by Alfr\'ed R\'enyi is discussed. The R\'enyi entropy is studied from the perspective of the geometry of the Lebesgue and generalised, exotic…
A way to pose the entropic uncertainty principle for trace-preserving super-operators is presented. It is based on the notion of extremal unraveling of a super-operator. For given input state, different effects of each unraveling result in…
Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy…