  The random matrix ensembles (RME) of quantum statistical Hamiltonian
operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random
matrix ensembles (Ginibre RME), are applied to following quantum statistical
systems: nuclear systems, molecular 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). The distribution function
for the random matrix ensembles is derived from the maximum entropy principle.
