Superstatistic properties of the cylindrical quantum dot

In this article, we investigate the magnetic and thermodynamic properties of a GaAs quantum dot with a cylindrical confinement potential, applying superstatistics methods. By solving the Schrödinger equation, we obtain the energy spectrum of the quantum system. We assume that the defined closed single-electron system is in a conditionally non-equilibrium state, where temperature is the fluctuating parameter, and its fluctuations correspond to a χ2 distribution. To describe the thermodynamic properties of this system, we applied the formalism of superstatistics. Based on this formalism, we derived a generalized partition function, which was then used to obtain expressions for the thermodynamic parameters. According to the obtained results, the influence of changing the values of the entropic index of non-extensive statistical mechanics on the behavior of thermodynamic parameters is most pronounced at low temperatures. As the temperature increases, this influence weakens and completely disappears at high temperatures. The thermodynamic parameters show completely anomalous behavior when the system deviates from the extensive state, i.e., when the entropic index of non-extensive statistical mechanics is not equal to one. At these values of the entropic index of non-extensive statistical mechanics heat capacity is negative at low temperatures, and entropy, which is normally an increasing quantity, decreases and reaches a certain minimum value. Such anomalous behavior of thermodynamic parameters disappears with increasing temperature, and at high temperatures, their behavior is similar to that of thermodynamic parameters in an extensive state.