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Nonextensive random-matrix theory based on Kaniadakis entropy

A. Y. Abul-Magd
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Abstract

The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element distributions as the previously obtained expression by using the Tsallis entropy, and the Abe entropy does not lead to a closed form expression, the Kaniadakis entropy leads to a new generalized form of the Wigner surmise that describes a transition of the spacing distribution from chaos to order. This expression is compared with the corresponding expression obtained by assuming Tsallis' entropy as well as the results of a previous numerical experiment.

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A. Y. Abul-Magd. 2006-09-19. Nonextensive random-matrix theory based on Kaniadakis entropy. https://doi.org/10.1016/j.physleta.2006.09.080

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