Several years ago, it has been discussed that non-logarithmic entropies such as the Tsallis q-entropy cannot be applied to systems with continuous variables. Now, in their recent paper [Phys. Rev. E 97, 012104 (2018)], Oikonomou and Bagci have modified the form of the q-entropy for discrete variables in such a way that its continuum limit exists. Here, it is shown that this modification violates the expandability property of entropy, and their work is actually a supporting evidence for the absence of the q-entropy for systems with continuous variables.
It has been known for some time that the usual $q$-entropy $S_q^{(n)}$ cannot be shown to converge to the continuous case. In [Phys. Rev. E 97 (2018) 012104], we have shown that the discrete $q$-entropy $\widetilde{S}_q^{(n)}$ converges to the continuous case when the total number of states are properly taken into account in terms of a convergence factor. Ou and Abe [Phys. Rev. E 97, (2018) 066101, arXiv:1801.03035] noted that this form of the discrete $q$-entropy does not conform to the Shannon-Khinchin expandability axiom. As a reply, we note that the fulfillment or not of the expandability …
Reply to Comments on "Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions"
Comment on ``Nonextensive hamiltonian systems follow Boltzmann's principle not Tsallis statistics-phase transition, second law of thermodynamics'' by Gross
Comment on Inconsistency of the basic nonadditivity of q-nonextensive statistical mechanics, arXiv:0910.3826v1
在最近的一篇论文中，王等人（2009）声称Tsallis的q-非广延统计力学的非可加性（Gell-Mann and Tsallis 2004，Tsallis 2009）在数学上是不一致的，因此应该仔细地全面回顾Tsallis的思想和理论。本文旨在指出Wang et al.（2009）的结论是通过误解两个基本项目得出的，因此Wang et al.的建议应该仔细审查。
This Reply is intended as a refutation of the preceding Comment [Oikonomou and Bagci, Phys. Rev. E 96, 056101 (2017)] on our paper [Plastino et al., Phys. Rev. E 94, 012145 (2016).]. We show that the Tsallis probability distribution of our paper does not coincide with the Tsallis distribution studied by Oikonomou and Bagci. Consequently, their findings do not apply to our paper.
Comment on: Thermostatistics of Overdamped Motion of Interacting Particles [arXiv:1008.1421]
在最近的一篇论文中，Phys. Rev. Lett. 105 260601（2010）[arXiv：1008.1421]，Andrade等人，他认为，在T=0时被限制在抛物阱中的经典粒子按照Tsallis统计分布。为了证明他们的观点，作者进行了分子动力学模拟。在这里，我们证明Andrade等人的模型可以精确求解。T=0时粒子的分布与Tsallis熵无关，而仅仅由力平衡决定。
Comment on "Troublesome aspects of the Renyi-MaxEnt treatment" by A. Plastino, M.C. Rocca and F. Pennini
Plastino，Rocca和Pennini [Phys. Rev. E \textbf{94}（2016）012145]最近指出，Rényi熵不适合使用泛函微积分进行热力学计算，因为它会导致与Tsallis熵不同的异常结果。我们首先表明，Tsallis熵也会导致这种异常行为，如果采用相同的功能演算方法。其次，我们注意到，拉格朗日乘子之一是设置在一个\textit{ad-hoc}的方式在功能演算方法的Plastino，Rocca和Pennini。最后，这些异常行为的解释提供了观察，由Plastino，Rocca和Pennini得到的广义分布不产生普通的正则配分函数在适当的限制，因此不能被认为是真正的广义分布。
In a recent paper [Entropy 2020, 22(1), 17] C. Tsallis states that entropy -- as in Shannon's or Kullback-Leiber's definitions -- is inadequate to interpret black hole entropy and suggests that a new non-additive functional should take the role of entropy. Here we counter argue by explaining the important distinction between the properties of extensivity and additivity, the latter is fundamental for entropy while the former is a property of particular thermodynamical systems that is not expected on black holes. We also point out other debatable statements in his analysis of black hole entropy.
