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Entropies based on fractional calculus. (English) Zbl 1231.82024
Summary: We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except additivity. We show that this entropy function satisfies the Lesche and thermodynamic stability criteria.
82B30Statistical thermodynamics
94A17Measures of information, entropy
60G22Fractional processes, including fractional Brownian motion
26A33Fractional derivatives and integrals (real functions)
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