One-Parameter Fisher–Rényi Complexity: Notion and Hydrogenic Applications
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AutorValero Toranzo, Irene; Sánchez-Moreno, Pablo; Rudnicki, Łukasz; Sánchez-Dehesa Moreno-Cid, Jesús
Information theoryFisher informationShannon entropyRényi entropyFisher-Rényi complexityHydrogenic systems
Valero Toranzo, I.; et al. One-Parameter Fisher–Rényi Complexity: Notion and Hydrogenic Applications. Entropy, 19(1): 16 (2017). [http://hdl.handle.net/10481/45204]
PatrocinadorThis work was partially supported by the Projects P11-FQM-7276 and FQM-207 of the Junta de Andalucia, and by the MINECO (Ministerio de Economía y Competitividad) and FEDER (European regional development fund) grants FIS2014- 54497P and FIS2014-59311P. Ł.R. acknowledges financial support by the grant number 2014/13/D/ST2/01886 of the National Science Center, Warsaw, Poland. Research in Cologne is supported by the Excellence Initiative of the German Federal and State Governments (Grant ZUK 81) and the DFG (GRO 4334/2-1). Ł.R. also acknowledges the support by the Foundation for Polish Science (FNP) and hospitality of the Freiburg Center for Data Analysis and Modeling. I.V.T. acknowledges the support of the Spanish Ministerio de Educación under the program FPU 2014.
In this work, the one-parameter Fisher–Rényi measure of complexity for general d-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic systems in terms of the quantum numbers of the quantum states and the nuclear charge.