A two-parameter generalization of Shannon-Khinchin axioms and the uniqueness theorem

DOI10.1016/j.physleta.2007.04.009zbMath1209.94027arXivcond-mat/0608139OpenAlexW2085248999MaRDI QIDQ715883

Hiroki Suyari, Tatsuaki Wada

Publication date: 19 April 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0608139

zbMATH Keywords

generalized entropyShannon-Khinchin axiomsShannon additivity

Mathematics Subject Classification ID

Difference operators (39A70) Measures of information, entropy (94A17)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• Axioms and uniqueness theorem for Tsallis entropy
• On some functional equations concerning entropy, directed divergence and inaccuracy
• Entropy of type \((\alpha,\beta)\) and other generalized measures in information theory
• A family of nonextensive entropies
• Generalization of Shannon–Khinchin Axioms to Nonextensive Systems and the Uniqueness Theorem for the Nonextensive Entropy
• A (p, q)-oscillator realization of two-parameter quantum algebras
• Generalization of Shannon’s theorem for Tsallis entropy
• Generalized information functions
• Non-linear kinetics underlying generalized statistics

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