Nonextensive random-matrix theory based on Kaniadakis entropy

TL;DR

This paper derives new eigenvalue distributions for random matrices using Kaniadakis entropy, revealing a transition from chaos to order, and compares it with other entropy-based models and numerical results.

Contribution

It introduces a novel random-matrix ensemble based on Kaniadakis entropy, providing a new generalized Wigner surmise for spectral spacing.

Findings

Kaniadakis entropy yields a new eigenvalue distribution form.

The derived distribution describes a transition from chaos to order.

Comparison shows consistency with numerical experiments.

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.