Distributions derived from the maximization of Rényi-Tsallis entropy are often called Tsallis’ distributions. We first indicate that these distributions can arise as mixtures, and can be interpreted as the solution of a standard maximum entropy problem with fluctuating constraints. Considering that Tsallis’ distributions appear for systems with displaced or fluctuating equilibriums, we show tha...

We consider the maximum entropy problems associated with Rényi Q-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The optimum maximum entropy probability distributions, which can exhibit a power-law behaviour, are der...

We consider a two-parameter family of Rényi relative entropies Dα,z(ρ||σ) that are quantum generalisations of the classical Rényi divergence Dα(p||q). This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum Rényi divergences, as well as the quantum Rényi relative entropies. All its members satisfy the quantum general...

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal2 hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L1 distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decre...

This paper is twofold. In the first part, we derive an improvement of the Rényi Entropy Power Inequality (EPI) recently obtained by Bobkov and Marsiglietti [10]. The proof largely follows Lieb’s [22] approach of employing Young’s inequality. In the second part, we prove a reverse Rényi EPI, that verifies a conjecture proposed in [4, 23] in two cases. Connections with various p-th mean bodies in...

Estimating entropies is important in many fields including statistical physics, machine learning and statistics. While the Shannon logarithmic entropy is the most fundamental, other Rényi entropies are also of importance. In this paper, we derive a bias corrected estimator for a subset of Rényi entropies. The advantage of the estimator is demonstrated via theoretical and experimental considerat...

A bstract In this work, we revisit the calculation of Rényi entropy in AdS 3 /(B)CFT 2 . We find that gravity solutions with brane intersection will lead to negative entropy.

The exact range of the joined values of several Rényi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied.