Recently, there has been significant interest in Rényi entropy power inequalities for several independent variables (the survey 12 is recommended to the reader for recent developments on forward and reverse EPIs).
But for q > 1 it lacks a property possessed by the Shannon entropy, and also by all Renyi entropies with q in, namely concavity. A definition of the Renyi entropy-power itself appears in, which is essentially Definition 5 below. So too is the corresponding Renyi entropy. Like the Kullback-Leibler divergence (Shannon relative entropy), the Renyi divergence is addititive or extensive in the sense thatĭ q(P 1 x P 2//Q 1 x Q 2) = D q(P 1//Q 1) + D q(P 2//Q 2). 27300934 DOI: 10.1103/PhysRevE.93. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. ( 1), for > 1 the Renyi entropies are given in terms of the log of the -norms (also known as lp-norms, where for. Via an introductory account of codes, we learn that "the Renyi divergence measures how much a probabilistic mixture of two codes can be compressed". Rnyi entropies are conceptually valuable and experimentally relevant generalizations of the celebrated von Neumann entanglement entropy. They appear in the form of unconditional and conditional entropies, relative entropies or mutual information, and have found many applications in information theory and beyond. In this sense the Shannon entropy has an operational definition as a compression rate and the Kolmogorov entropy has an operational definition as shortest program describing data. The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. To us an operational definition of a quantity means that the quantity is the natural way to answer a natural question and that the quantity can be estimated by feasible measurements combined with a reasonable number of computations. Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the Rnyi entropy. Harremöes is looking for an information theoretic interpretation of the Renyi entropies in terms of what he calls an operational definition: Much of the analysis about the Shannon and Rnyi entropies is. Following the discussion we had here about the merits of Tsallis and Renyi entropies, here's an interesting paper by Peter Harremöes - Interpretations of Renyi Entropies And Divergences. p(x) logp(x)dx with entropy power N1 N e2h (provided that Nr(X) > 0 for some r > 1).
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