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Rényi and Tsallis entropies for incomplete or overcomplete systems of events

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  • Campos, Diógenes

Abstract

In this article, Shannon, Rényi and Tsallis entropies are considered for a system of events characterized by an arbitrary probability distribution P that can be incomplete, complete or overcomplete. After a suitable transformation that leads to the escort probabilities of P, these can be written as the canonical probability distribution for a set of pseudo-energies (Hartley information, En=−lnPn) and a dimensionless parameter q that plays the role of thermodynamics β. Several relations between the entropies are presented, including the analysis of compound systems. The method is illustrated with an example.

Suggested Citation

  • Campos, Diógenes, 2010. "Rényi and Tsallis entropies for incomplete or overcomplete systems of events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 981-992.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:5:p:981-992
    DOI: 10.1016/j.physa.2009.11.011
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    Cited by:

    1. Campos, Diógenes, 2011. "A thermodynamic-like approach for the study of probabilistic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 214-222.
    2. Campos, Diógenes, 2011. "A thermodynamic-like characterization of Colombia’s presidential elections in 2010, and a comparison with other Latin American countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1779-1790.
    3. Campos, Diógenes, 2010. "Real and spurious contributions for the Shannon, Rényi and Tsallis entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3761-3768.

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