The q-exponentials do not maximize the Rényi entropy
Oikonomou T. Kaloudis K. Bagci G.B.
15 September 2021Elsevier B.V.
Physica A: Statistical Mechanics and its Applications
2021#578
It is generally assumed that the Rényi entropy is maximized by the q-exponentials and is hence useful to construct a generalized statistical mechanics. However, to the best of our knowledge, this assumption has never been explicitly checked. In this work, we consider the Rényi entropy with the linear and escort mean value constraints and check whether it is indeed maximized by q-exponentials. We show, both theoretically and numerically, that the Rényi entropy yields erroneous inferences concerning the optimum distributions of the q-exponential form and moreover exhibits high estimation errors in the regime of long range correlations. Finally, we note that the Shannon entropy successfully detects the power law distributions when the logarithmic mean value constraint is used.
Estimation error , Estimators , MaxEnt , Optimum distribution , q-exponentials , Rényi entropy , Shannon entropy
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College of Engineering and Computer Science, VinUniversity, Hanoi, 10000, Viet Nam
Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
Department of Physics, Mersin University, Mersin, 33343, Turkey
College of Engineering and Computer Science
Department of Mathematics
Department of Physics
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