Superstatistics of anisotropic oscillator in a noncommutative plane

In this work, we study anisotropic oscillator in a noncommutative plane. We first, obtain the exact energy values as a function of noncommutative parameter theta. Using these energy values, we also investigate the superstatistical thermodynamic functions associated with the model. The superstatistical partition function is expressed as a double series and the convergence of double series is tested for the q-deformed Dirac delta distribution function. Also, convergent series is expressed up to second order of inverse temperature (beta = 1/(k(B)T)) by the Euler-Maclaurin formula and compare with direct summation over possible bound states up to certain approximation. In-addition, superstatistics and well-known thermal statistics of anisotropic oscillator are compared and three special cases in commutative and noncommutative spaces are investigated. Moreover, superstatistics and ordinary statistics examine at low and high temperatures. The effect of theta, beta and deformation parameter q on thermal properties are investigated at low and high temperatures.