Striving to find a bridge between noncommutative and generalized entropy parameters in harmonic oscillator dynamics

Abstract

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 Rényi entropy measures. The primary objective is to examine the possibility of an intrinsic link and mutual influence between the noncommutative parameter( θ) and the parameters arising from generalized entropies. By analyzing both Tsallis and Rényi frameworks, we investigate whether a fundamental relationship exists between θ and the entropy index q. Establishing such a connection could provide new insights into the interplay between spacetime geometry and generalized statistical mechanics.