A Brief Review of Generalized Entropies
Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/20/11/813 |
| _version_ | 1811186300124921856 |
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| author | José M. Amigó Sámuel G. Balogh Sergio Hernández |
| author_facet | José M. Amigó Sámuel G. Balogh Sergio Hernández |
| author_sort | José M. Amigó |
| collection | DOAJ |
| description | Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon⁻Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances. |
| first_indexed | 2024-04-11T13:43:15Z |
| format | Article |
| id | doaj.art-a34adee460d94dd6a8a54bbdf61e7161 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:43:15Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a34adee460d94dd6a8a54bbdf61e71612022-12-22T04:21:10ZengMDPI AGEntropy1099-43002018-10-01201181310.3390/e20110813e20110813A Brief Review of Generalized EntropiesJosé M. Amigó0Sámuel G. Balogh1Sergio Hernández2Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad s/n, 03202 Elche, SpainDepartment of Biological Physics, Eötvös University, H-1117 Budapest, HungaryHCSoft Programación S.L., 30007 Murcia, SpainEntropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon⁻Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.https://www.mdpi.com/1099-4300/20/11/813generalized entropyTsallisRényiHanel–Thurner exponentsnon-stationary regime |
| spellingShingle | José M. Amigó Sámuel G. Balogh Sergio Hernández A Brief Review of Generalized Entropies Entropy generalized entropy Tsallis Rényi Hanel–Thurner exponents non-stationary regime |
| title | A Brief Review of Generalized Entropies |
| title_full | A Brief Review of Generalized Entropies |
| title_fullStr | A Brief Review of Generalized Entropies |
| title_full_unstemmed | A Brief Review of Generalized Entropies |
| title_short | A Brief Review of Generalized Entropies |
| title_sort | brief review of generalized entropies |
| topic | generalized entropy Tsallis Rényi Hanel–Thurner exponents non-stationary regime |
| url | https://www.mdpi.com/1099-4300/20/11/813 |
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