Entropy, Maximum Entropy Priciple and quantum statistical information for various random matrix ensembles

TL;DR

This paper explores the application of maximum entropy principles to derive distribution functions for various quantum random matrix ensembles, linking entropy concepts with quantum chaos and integrability measures.

Contribution

It introduces a quantum statistical information functional based on negentropy and derives distribution functions from the maximum entropy principle for different RME.

Findings

Distribution functions derived from maximum entropy principle.

Measures of quantum chaos and integrability defined.

Application to various quantum systems and ensembles.

Abstract

The random matrix ensembles (RME) of quantum statistical Hamiltonians, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied in literature to following quantum statistical systems: molecular systems, nuclear systems, disordered materials, random Ising spin systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). Entropy is neginformation (opposite of information or minus information. The distribution functions for the random matrix ensembles are derived from the maximum entropy principle.