In this work, we investigate the cumulative effects of laser and spin-orbit interaction (SOI) on the thermodynamic properties of a quantum pseudo-dot using the Tsallis formalism, through the evaluation of the energy to derive some thermodynamic properties at the accessible states. From the results obtained, we found that contrary to the SOI, a laser field is a suitable external field to reduce the rate of entropy (disorder) in a quantum system, and thus, this allows control on the spin alignment and increasing the number of accessible states hence stabilizing our system, simultaneously reducing the rate of entropy due to the great effect of the laser field. Therefore, the combined effects of laser field and SOI are an important parameter to enhance the thermodynamic quantities and more define the spin alignment of quantum system.

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In this work, we investigated the influence of the geometrical confinement effects on the fundamental thermal properties of rutile and anatase TiO2 for both cylindrical nanostructures (CNSs) and nanotubular structures (NTSs), respectively. Calculations of energy levels are developed in the framework of effective mass approximation by generalizing the resolution of Schrödinger equation in a truncated cylinder. The energy spectrum is then used in the determination of thermodynamic properties by using the Boltzmann-Gibbs distribution. Numerical computations done for both rutile and anatase TiO2 nanomaterials reveal a strong localization of the electron orbitals along to the lateral surface for all the studied are CNS and NTS. The average energy, heat capacity, entropy, and Helmholtz free energy calculated for different thicknesses for NTS and different cross-sections of CNS. Our numerical investigation shows that all thermodynamic properties depend on the temperature, the cross-section for the CNS, and the shell thickness for the NTS. We demonstrated that for low thickness, the heat capacity shows a Schottky-like anomaly at low temperatures. We also show that the Rutile structure is more stable than anatase. We hope that the thermodynamic properties concluded from this study can be considered as useful information for understanding the thermodynamic properties of TiO2 nanofibers.