Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems
| العنوان: | Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems |
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| المؤلفون: | Constantino Tsallis |
| المصدر: | Entropy Volume 17 Issue 5 Pages 2853-2861 Entropy, Vol 17, Iss 5, Pp 2853-2861 (2015) |
| بيانات النشر: | arXiv, 2014. |
| سنة النشر: | 2014 |
| مصطلحات موضوعية: | Path (topology), Discrete mathematics, Logarithm, Statistical Mechanics (cond-mat.stat-mech), Generalization, General Physics and Astronomy, Order (ring theory), FOS: Physical sciences, lcsh:Astrophysics, Basis (universal algebra), Statistical mechanics, lcsh:QC1-999, nonadditive entropies, lcsh:QB460-466, strongly correlated random variables, lcsh:Q, Shore and Johnson axioms, Uniqueness, nonextensive statistical mechanics, lcsh:Science, lcsh:Physics, Axiom, Condensed Matter - Statistical Mechanics, Mathematics |
| الوصف: | It is by now well known that the Boltzmann-Gibbs-von Neumann-Shannon logarithmic entropic functional ((S_{BG})) is inadequate for wide classes of strongly correlated systems: see for instance the 2001 Brukner and Zeilinger's {it Conceptual inadequacy of the Shannon information in quantum measurements}, among many other systems exhibiting various forms of complexity. On the other hand, the Shannon and Khinchin axioms uniquely mandate the BG form (S_{BG}=-ksum_i p_i ln p_i) the Shore and Johnson axioms follow the same path. Many natural, artificial and social systems have been satisfactorily approached with nonadditive entropies such as the (S_q=k frac{1-sum_i p_i^q}{q-1}) one ((q in {cal R} S_1=S_{BG})), basis of nonextensive statistical mechanics. Consistently, the Shannon 1948 and Khinchine 1953 uniqueness theorems have already been generalized in the literature, by Santos 1997 and Abe 2000 respectively, in order to uniquely mandate (S_q). We argue here that the same remains to be done with the Shore and Johnson 1980 axioms. We arrive to this conclusion by analyzing specific classes of strongly correlated complex systems that await such generalization. |
| وصف الملف: | application/pdf |
| DOI: | 10.48550/arxiv.1404.1257 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d40392429fbcbe26f7fc547e6764e76Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....7d40392429fbcbe26f7fc547e6764e76 |
| قاعدة البيانات: | OpenAIRE |
| DOI: | 10.48550/arxiv.1404.1257 |
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