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Thermodynamics Properties of Confined Particles on Noncommutative Plane

We consider a system of $N$ particles living on the noncommutative plane in the presence of a confining potential and study its thermodynamics properties. Indeed, after calculating the partition function, we determine the corresponding internal energy and heat capacity where different corrections are obtained. In analogy with the magnetic field case, we define an effective magnetization and study its susceptibility in terms of the noncommutative parameter $θ$. By introducing the chemical potential, we investigate the Bose-Einstein condensation for the present system. Different limiting cases related to the temperature and $θ$ will be analyzed as well as some numerical illustration will be presented.