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Novel quantization properties related to the state vectors and the energyspectrum of a two-dimensional system of free particles are obtained in theframework of noncommutative (NC) quantum mechanics (QM) supported by theWeyl-Wigner formalism. Besides reproducing the magnetic field aspect of aZeeman-like effect, the momentum space NC parameter introduces mutualinformation properties quantified by the quantum purity related to the relevantcoordinates of the corresponding Hilbert space. Supported by the QM in thephase-space, the thermodynamic limit is obtained, and the results are extendedto three-dimensional systems. The noncommutativity imprints on thethermodynamic variables related to free particles are identified and, afterintroducing some suitable constraints to fix an axial symmetry, the analysis isextended to two- and- three dimensional quantum rotor systems, for which thequantization aspects and the deviation from standard QM results are verified.

Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors