  Novel quantization properties related to the state vectors and the energy
spectrum of a two-dimensional system of free particles are obtained in the
framework of noncommutative (NC) quantum mechanics (QM) supported by the
Weyl-Wigner formalism. Besides reproducing the magnetic field aspect of a
Zeeman-like effect, the momentum space NC parameter introduces mutual
information properties quantified by the quantum purity related to the relevant
coordinates of the corresponding Hilbert space. Supported by the QM in the
phase-space, the thermodynamic limit is obtained, and the results are extended
to three-dimensional systems. The noncommutativity imprints on the
thermodynamic variables related to free particles are identified and, after
introducing some suitable constraints to fix an axial symmetry, the analysis is
extended to two- and- three dimensional quantum rotor systems, for which the
quantization aspects and the deviation from standard QM results are verified.
