Striving to find a bridge between noncommutative and generalized entropy parameters in the harmonic oscillator dynamics
In this study, we use the harmonic oscillator s energy spectrum to connect its dynamical behavior to the formalism of statistical mechanics through entropy. We perform a thermal analysis of the entropy generated by this spectrum in both commutative and noncommutative two-dimensional configuration spaces, employing the Tsallis and Renyi entropy measures. The primary objective is to examine the possibility of an intrinsic link and mutual influence between the noncommutative parameter({\theta}) and the parameters arising from generalized entropies. By analyzing both Tsallis and Renyi frameworks, we investigate whether a fundamental relationship exists between {\theta} and the entropy index q. Establishing such a connection could provide new insights into the interplay between spacetime geometry and generalized statistical mechanics.