A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings
Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also v...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-05-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/7/2/29 |
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| author | María-Jesús Campión Cristina Gómez-Polo Esteban Induráin Armajac Raventós-Pujol |
| author_facet | María-Jesús Campión Cristina Gómez-Polo Esteban Induráin Armajac Raventós-Pujol |
| author_sort | María-Jesús Campión |
| collection | DOAJ |
| description | Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations. |
| first_indexed | 2024-12-13T01:45:03Z |
| format | Article |
| id | doaj.art-5926259b0f7e4ec8947e521aab7c09f0 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-13T01:45:03Z |
| publishDate | 2018-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5926259b0f7e4ec8947e521aab7c09f02022-12-22T00:03:39ZengMDPI AGAxioms2075-16802018-05-01722910.3390/axioms7020029axioms7020029A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and OrderingsMaría-Jesús Campión0Cristina Gómez-Polo1Esteban Induráin2Armajac Raventós-Pujol3Institute for Advanced Research in Business and Economics (Inarbe), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, SpainInstitute for Advanced Materials (InaMat), Departamento de Física, Universidad Pública de Navarra, 31006 Pamplona, SpainInstitute for Advanced Materials (InaMat), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, SpainInstitute for Advanced Research in Business and Economics (Inarbe), Departamento de Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, SpainDifferent abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations.http://www.mdpi.com/2075-1680/7/2/29ordered structuresnumerical representationsentropyrepresentabilityutility functions |
| spellingShingle | María-Jesús Campión Cristina Gómez-Polo Esteban Induráin Armajac Raventós-Pujol A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings Axioms ordered structures numerical representations entropy representability utility functions |
| title | A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings |
| title_full | A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings |
| title_fullStr | A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings |
| title_full_unstemmed | A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings |
| title_short | A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings |
| title_sort | survey on the mathematical foundations of axiomatic entropy representability and orderings |
| topic | ordered structures numerical representations entropy representability utility functions |
| url | http://www.mdpi.com/2075-1680/7/2/29 |
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