Superstatistics of the one-dimensional Klein-Gordon oscillator with energy-dependent potentials

In this paper, we investigate the influence of energy-dependent potentials on the thermodynamic properties of the Klein-Gordon oscillator (KGO). With the obtained energy eigenvalues, all the thermal properties of the system have been calculated using the well-known Euler-Maclaurin method. The investigation is extended to the study of the Superstatistics properties of the system. The probability density f(beta) follows chi(2) Superstatistics (Tsallis statistics or Gamma distribution) for the system. Under the approximation of the low-energy asymptotics of Superstatistics, we calculated partition function and other thermal properties of the system. This approximation leads to a universal parameter q for any Superstatistics, not only for Tsallis statistics. By using the desired partition function, all thermal properties have been obtained in terms of this parameter. Also, the influence of the potentials on the thermal properties, via the parameter gamma, are well discussed.