In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, the...

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 is equally suitable to describe those systems with powerlaw behaviour, where the use of the Tsallis entropy is relevant. We discuss a specific class of dynam...

1.2 Erdős-Renyi Model The above approach constitutes the sampling view of generating a random graph. Alternatively we can take a constructive view where we start with vertex set V = {1, 2, 3....n}, and selecting uniformly at random one edge from those edges not yet chosen, repeating this m times. Definition 3 G(n, p) is the random graph obtained by starting with vertex set V = {1, 2, 3...n}, le...

We revisit the problem of estimating entropy of discrete distributions from independent samples, studied recently by Acharya, Orlitsky, Suresh and Tyagi (SODA 2015), improving their upper and lower bounds on the necessary sample size n. For estimating Renyi entropy of order α, up to constant accuracy and error probability, we show the following Upper bounds n = O(1) · 2(1− 1 α )Hα for integer α...

This paper studies the complexity of estimating Renyi divergences of a distribution p observed from samples, with respect to a baseline distribution q known a priori. Extending the results of Acharya et al. (SODA’15) on estimating Renyi entropy, we present improved estimation techniques together with upper and lower bounds on the sample complexity. We show that, contrarily to estimating Renyi e...

General relations are found between the measure of the uniformity of distributions on the phase space and the first moments and correlations of extensive variables for systems close to thermal equilibrium. The role played by the parameter of the Renyi entropy for the analysis of their fluctuations and correlations is studied. Analytical results are verified and illustrated by direct simuations ...