2006/09/19 by A. Y. Abul-Magd
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Computer science #Eigenvalues and eigenvectors #Entropy (arrow of time) #Expression (computer science) #Joint entropy #Mathematics #Maximum entropy probability distribution #Physics #Principle of maximum entropy #Quantum mechanics #Random matrix #Rényi entropy #Statistical Mechanics and Entropy #Statistical physics #Statistics #Tsallis entropy #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physleta.2006.09.080
published as Phys. Lett. A 361, 450 (2007) · 10 pages, 2 figures
arxiv created 2006/09/19 · openalex publication_date 2006/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.