  The review begins with a consideration of 3 forms of quantum information
entropy associated with Shannon and Jaynes. For model two-electron spin
compensated systems, some analytic progress is first reported. The Jaynes
entropy is clearly related to correlation kinetic energy. A way of testing the
usefulness of a known uncertainty principle inequality is proposed for a whole
class of model two-electron atoms with harmonic confinement but variable
electron-electron interaction. Emerging properties are then studied by
reference to bcc Na at ambient pressure and its modeling by `jellium'. Jellium
itself has collective behaviour with changes of the density, especially
noteworthy being the discontinuity of the momentum distribution at the Fermi
surface. This has almost reduced to zero at $r_s = 100$ a.u., the neighbourhood
in which the quantal Wigner electron solid transition is known to occur.
However, various workers have studied crystalline Na under pressure and their
results are compared and contrasted. Work by DFT on K, Rb, and Cs is discussed,
but now with reduced density from the ambient pressure value. The crystalline
results for the cohesive energy of these metals as a function of lattice
parameters and local coordination number are shown to be closely reproduced by
means of ground and excited states for dimer potential energy curves. Then,
pair potentials for liquid Na and Be are reviewed, and compared with the
results of computer simulations from the experimental structure factor for Na.
Finally, magnetic field effects are discussed. First a phenomenological model
of the metal-to-insulator transition is presented with an order parameter which
is the discontinuity in the Fermi momentum distribution. Lastly, experiments on
a two-dimensional electron assembly in a GaAs/AlGaAs heterojunction in a
perpendicular magnetic field are briefly reviewed and then interpreted.
