The superposition of different statistics defines the concept of superstatistics, which makes an equilibrium statistical mechanics incorporate fluctuations. Herein, we study the thermodynamical properties of the anharmonic oscillator for Dirac equation in commutative and noncommutative (NC) spaces using q-deformed superstatistics. By employing the biconfluent Heun functions, the energy spectrum and the wave functions of the considered system are expressed in explicit form. Moreover, the thermodynamical properties of the anharmonic oscillator ensemble in terms of the effective Boltzmann factor are derived, and in order to illustrate the results, some figures are plotted for the clarity of our results.

不同统计量的叠加定义了超统计量的概念，这使均衡统计力学包含了波动。在此，我们使用q变形超统计量研究了换向和非换向（NC）空间中Dirac方程的非谐振子的热力学性质。通过采用双汇合的Heun函数，所考虑系统的能谱和波函数以明确的形式表示。此外，根据有效的玻尔兹曼因子，得出了非谐振荡器集合的热力学性质，并且为了说明结果，为清楚起见，绘制了一些数字。