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Real and spurious contributions for the Shannon, Rényi and Tsallis entropies

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  • Campos, Diógenes

Abstract

A two-parameter probability distribution is constructed by dilatation (or contraction) of the escort probability distribution. This transformation involves a physical probability distribution P associated with the system under study and an almost arbitrary reference probability distribution P′. In contrast to the Shannon and Rényi entropies, the Tsallis entropy does not decompose as the sum of the physical contribution due to P and the reference or spurious part owing to P′. For solving this problem, a slight modification to the relation between Tsallis and Rényi entropies must be introduced. The procedure in this paper gives rise to a nonconventional one-parameter Shannon entropy and to two-parameter Rényi and Tsallis entropies associated with P. It also contributes to clarify the meaning and role of the escort probabilities set.

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  • 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.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:18:p:3761-3768
    DOI: 10.1016/j.physa.2010.05.029
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    References listed on IDEAS

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    1. Beck, Christian, 2004. "Superstatistics, escort distributions, and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 139-144.
    2. 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.
    3. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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    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.

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