Nonextensive and superstatistical generalizations of random-matrix theory

TL;DR

This paper reviews nonextensive and superstatistical generalizations of random matrix theory, which incorporate correlations and non-standard entropies, and demonstrates their effectiveness in modeling systems transitioning from order to chaos.

Contribution

It introduces and reviews generalized RMT frameworks based on non-extensive entropies and superstatistics, expanding the theory's applicability to correlated systems.

Findings

Calculated nearest-neighbor-spacing distributions match experimental data.

Generalized RMT models better describe systems transitioning from order to chaos.

Demonstrated the value of these generalizations through comparison with numerical experiments.

Abstract

Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep base invariance on the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or following the basic prescription of the recently suggested concept of superstatistics. We review these generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments and numerical-experiments on systems in transition from order to chaos.