Thermodynamic Signatures of a Dunkl–Pauli Oscillator under Aharonov–Bohm Flux

We investigate a two-dimensional Dunkl–Pauli oscillator in the presence of Aharonov–Bohm (AB) flux, focusing on the interplay between reflection symmetry and topological gauge effects. The model is formulated by introducing Dunkl operators into the Pauli Hamiltonian, which incorporates both spin interactions and a singular magnetic flux confined to a flux tube. By solving the stationary eigenvalue problem with appropriate boundary and regularity conditions, we show that the combined action of Dunkl deformation and AB flux imposes a nontrivial constraint on the admissible quantum states.

This constraint leads to the emergence of a lowest allowed angular quantum number, which depends explicitly on the flux and reflection parameters and effectively restructures the Hilbert space rather than producing a simple shift in the energy spectrum. Using the exact energy eigenvalues, we construct the canonical partition function and derive the corresponding thermodynamic quantities, including internal energy, entropy, and heat capacity.

The thermodynamic behavior reveals clear signatures of the spectral constraint: at low temperatures, the system is dominated by the modified ground state, while the heat capacity exhibits a flux-dependent Schottky-type anomaly. At high temperatures, the system approaches the classical oscillator limit. These findings highlight how the interplay between Dunkl symmetry and topological flux can generate observable thermodynamic effects, with potential applications in mesoscopic quantum systems and engineered gauge-field environments.