Composability in a certain family of entropies
Henrik Densing Petersen
TL;DR
This paper demonstrates that within a specific class of entropy functions, only Tsallis entropies satisfy the property of composability under certain conditions, highlighting their unique mathematical structure.
Contribution
It proves the uniqueness of Tsallis entropies in satisfying composability among entropies of the form H(P)=-∑i f(p_i) with specific assumptions on f.
Findings
Tsallis entropies are uniquely composable within their class.
The paper establishes conditions under which entropy functions are composable.
It clarifies the mathematical structure of entropy functions related to composability.
Abstract
It is shown that the Tsallis entropies are the only entropies of the form , with suitable assumptions on , satisfying the condition of composability.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Thermodynamics and Statistical Mechanics · Fractional Differential Equations Solutions