A generalized Faddeev's axiom and the uniqueness theorem for Tsallis entropy
Shigeru Furuichi
TL;DR
This paper proves a new, simpler uniqueness theorem for Tsallis entropy using a generalized Faddeev's axiom, improving upon previous results by simplifying the axiomatic foundation.
Contribution
It introduces a generalized Faddeev's axiom that simplifies the proof of the uniqueness of Tsallis entropy, enhancing the theoretical understanding of entropy measures.
Findings
Proves the uniequness theorem for Tsallis entropy
Introduces a simpler axiomatic framework
Improves upon previous uniqueness results
Abstract
The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev's axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin's axiom in \cite{Suy}, in the sence that our axiom is simpler than his one, as similar that Faddeev's axiom is simpler than Shannon-Khinchin's one.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Statistical Methods and Models · Complex Systems and Time Series Analysis