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International Journal of Quantum Chemistry

Inequalities for phase‐space Rényi entropies

István Hornyák, Ágnes Nagy

Published May 11, 2011• 11 citations
Publisher

Abstract

Abstract Relations between different kinds of phase‐space Rényi and Shannon entropies are proved. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
DOI
10.1002/qua.23126

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In this study, the information‐theoretic measures in both the position and momentum spaces for the pseudoharmonic potential using Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy, and Onicescu information energy are investigated analytically and numerically. The results obtained are applied to some diatomic molecules. The Renyi and Tsallis entropies are analytically obtained in position space using Srivastava–Niukkanen linearization formula in terms of the Lauricella hypergeometric function. Also, they are obtained in the momentum space in terms of the multivariate Bell polynomials of Combinatorics. We observed that the Fisher information increases with n in both the position and momentum spaces, but decreases with for all the diatomic molecules considered. The Shannon entropy also increases with increasing n in the position space and decreases with increasing . The variations of the Renyi and Tsallis entropies with are also discussed. The exact and numerical values of the Onicescu information energy are also obtained, after which the ratio of information‐theoretic impetuses to lengths for Fisher, Shannon, and Renyi are obtained. © 2015 Wiley Periodicals, Inc.