  Random matrix ensembles (RME) of quantum statistical Hamiltonian operators,
{\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix
ensembles (Ginibre RME), found applications in literature in study of following
quantum statistical systems: molecular systems, nuclear systems, disordered
materials, random Ising spin systems, quantum chaotic 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.
