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Entropy 2018, 20(12), 940; https://doi.org/10.3390/e20120940

Associating an Entropy with Power-Law Frequency of Events

1
Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil
2
La Plata National University and Argentina’s National Research Council (IFLP-CCT-CONICET)-C. C. 727, La Plata 1900, Argentina
*
Author to whom correspondence should be addressed.
Received: 3 October 2018 / Revised: 19 November 2018 / Accepted: 23 November 2018 / Published: 6 December 2018
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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Abstract

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy S q . The relevant parameters become: (i) The entropic index q, which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ε 0 , in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature T q with k T q ε 0 (i.e., isothermal processes, for a given q), in analogy with those in the class of self-organized criticality, which are known to occur at fixed temperatures. Typical examples are analyzed, like earthquakes, avalanches, and forest fires, and in some of them, the entropic index q and value of T q are estimated. The knowledge of the associated entropic form opens the possibility for a deeper understanding of such phenomena, particularly by using information theory and optimization procedures. View Full-Text
Keywords: self-organized criticality; generalized entropies; nonextensive thermostatistics; information theory self-organized criticality; generalized entropies; nonextensive thermostatistics; information theory
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Curado, E.M.F.; Nobre, F.D.; Plastino, A. Associating an Entropy with Power-Law Frequency of Events. Entropy 2018, 20, 940.

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