Associating an Entropy with Power-Law Frequency of Events

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 Sq. The relevant...

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Authors: Curado, Evaldo M. F., Nobre, Fernando D., Plastino, Ángel Luis
Format: article
Status:Published version
Publication Date:2018
Country:Argentina
Institution:Universidad Nacional de La Plata
Repository:SEDICI (UNLP)
Language:English
OAI Identifier:oai:sedici.unlp.edu.ar:10915/78645
Online Access:http://sedici.unlp.edu.ar/handle/10915/78645
Access Level:Open access
Keyword:Física
self-organized criticality
generalized entropies
nonextensive thermostatistics
Information theory
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spelling Associating an Entropy with Power-Law Frequency of EventsCurado, Evaldo M. F.Nobre, Fernando D.Plastino, Ángel LuisFísicaself-organized criticalitygeneralized entropiesnonextensive thermostatisticsInformation theoryEvents 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 Sq. 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 #0, in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature Tq with kTq µ #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 Tq 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.Facultad de Ciencias ExactasInstituto de Física La Plata2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/78645enginfo:eu-repo/semantics/altIdentifier/doi/10.3390/e20120940info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2024-05-08T12:52:29Zoai:sedici.unlp.edu.ar:10915/78645Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292024-05-08 12:52:29.804SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Associating an Entropy with Power-Law Frequency of Events
title Associating an Entropy with Power-Law Frequency of Events
spellingShingle Associating an Entropy with Power-Law Frequency of Events
Curado, Evaldo M. F.
Física
self-organized criticality
generalized entropies
nonextensive thermostatistics
Information theory
title_short Associating an Entropy with Power-Law Frequency of Events
title_full Associating an Entropy with Power-Law Frequency of Events
title_fullStr Associating an Entropy with Power-Law Frequency of Events
title_full_unstemmed Associating an Entropy with Power-Law Frequency of Events
title_sort Associating an Entropy with Power-Law Frequency of Events
dc.creator.none.fl_str_mv Curado, Evaldo M. F.
Nobre, Fernando D.
Plastino, Ángel Luis
author Curado, Evaldo M. F.
author_facet Curado, Evaldo M. F.
Nobre, Fernando D.
Plastino, Ángel Luis
author_role author
author2 Nobre, Fernando D.
Plastino, Ángel Luis
author2_role author
author
dc.subject.none.fl_str_mv Física
self-organized criticality
generalized entropies
nonextensive thermostatistics
Information theory
topic Física
self-organized criticality
generalized entropies
nonextensive thermostatistics
Information theory
description 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 Sq. 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 #0, in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature Tq with kTq µ #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 Tq 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.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/78645
url http://sedici.unlp.edu.ar/handle/10915/78645
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3390/e20120940
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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