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.

For a large class of stationary probability measures on AN, where A is a finite alphabet, we compute the specific Rényi entropy of order α and the specific guesswork moments of order β > −1. We show that the specific guesswork moment of order β equals the specific Rényi entropy of order α = 1/(1+ β) multiplied by β. The method is based on energy–entropy estimates suggested by statistical physic...

A hidden Markov process (HMP) is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. The non-asymptotic equipartition property (NEP) is a bound on the probability of the sample entropy deviating from the entropy rate of a stochastic process, so it can be viewed as a refinement of Shannon-McMillan-Breiman theorem. In this report, w...

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p > 1, the minimum output Rényi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Rényi entropy of order p for a product channel need not be significantly greater than the minimum output entr...

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...