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Rényi Entropy and Complexity

  • Á. Nagy
  • E. Romera

Abstract

Several important properties of the Rényi entropy and Rényi entropy power are presented. Uncertainty relations for the Rényi entropy including uncertainty relations for single particle densities of many particle systems in position and momentum spaces are discussed. Connection between Fisher information and Rényi entropy is studied. The Fisher-Rényi information plane and entropic product are presented.

Position and momentum space Rényi entropies of order α are presented for ground-state neutral atoms with atomic numbers Z=1–103. It is emphasized that the values of α≤1 (α≥1) stress the shell structure for position-space (momentum-space) Rényi entropies. Position and momentum space relative Rényi entropies of order α are presented for ground-state neutral atoms with atomic numbers Z=1–103. Simple hydrogen-like model densities are used as the reference. A relationship with the atomic radius and quantum capacitance is also discussed.

The relationship between the statistical complexity and the Rényi entropy is studied. A recently introduced, one-parameter extension of the LMC complexity is presented.

The maximum Rényi entropy principle is used to generalize the Thomas-Fermi model. A simple relation between the dimension and the Rényi parameter is emphasized.

Keywords

Uncertainty Relation Momentum Space Fisher Information Shannon Entropy Model Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

E.R. acknowledges the Spanish project FQM-165/0207 (Junta de Andalucía) and No. FIS2008-01143. Á.N. acknowledges grant OTKA No. T67923. The work was also supported by the TAMOP 4.2.1/B-09/1/KONV-2010-0007 project. The project is co-financed by the European Union and the European Social Fund.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsUniversity of DebrecenDebrecenHungary
  2. 2.Departamento de Física Atómica, Molecular y NuclearUniversidad de GranadaGranadaSpain

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