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In this paper, we study the thermodynamic properties of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) for both relativistic and nonrelativistic cases in the high temperatures regime. Thus, we use the canonical ensemble for a set of N -particles in contact with a thermal bath. Next, we explicitly determine the thermodynamic properties of our interest, namely: the Helmholtz free energy, the entropy, the mean energy, and the heat capacity. In order to perform the calculations, we work with the Euler-MacLaurin formula to construct the partition function of the system. In that way, we plotted the graphs of thermodynamic properties as a function of temperature for six different values of the magnetic field and of the NC parameters. As a result, we note that the Helmholtz free energy decreases with the temperature, increases with the NC parameters, and can decrease or increase for certain values of the magnetic field, white that the entropy increases with the temperature, decreases with the NC parameters, and can decrease or increase for certain values of the magnetic field. Besides, the mean energy increases linearly with the temperature and its values for the relativistic case are twice of the nonrelativistic case, consequently, the heat capacity for the relativistic case is twice of the nonrelativistic case, where both are constants, and therefore, satisfying the so-called Dulong-Petit law. Finally, we also verify that there is no influence of the AMM on the thermodynamic properties of the system.

In the present paper, we investigate the bound-state solutions of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning cosmic string (CS) spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case). In particular, in the first two scenarios, we have an inertial frame, while in the third, we have a rotating frame. With respect to bound-state solutions, we focus primarily on eigenfunctions (Dirac spinor and wave function) and on energy eigenvalues (Landau levels), where we use the flat and curved Dirac equation in polar coordinates to reach such solutions. However, unlike the literature, here we consider a CS with an angular momentum non-null and also the NC of the positions, and therefore, we seek a more general description for the QHE. Once the solutions are obtained, we discuss the influence of all parameters and physical quantities on relativistic energy levels. Finally, we analyze the nonrelativistic limit, and we also compared our problem with other works, where we verified that our results generalize some particular cases of the literature.