  The random matrix ensembles (RMT) 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's electrostatic analogy). The Ginibre ensemble of
nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system
described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the
Hamiltonian are complex-valued random variables. The second difference of
complex eigenenergies is viewed as discrete analog of Hessian with respect to
labelling index. The results are considered in view of Wigner and Dyson's
electrostatic analogy. An extension of space of dynamics of random magnitudes
is performed by introduction of discrete space of labeling indices. The
comparison with the Gaussian ensembles of random hermitean Hamiltonian matrices
$H$ is performed. Measures of quantum chaos and quantum integrability with
respect to eigenergies of quantum systems are defined and they are calculated.
  Quantum statistical information functional is defined as negentropy (opposite
of von Neumann's entropy or minus entropy). The probability distribution
functionals for the random matrix ensembles (RMT) are derived from the maximum
entropy principle.
