The minimal length uncertainty and the nonextensive thermodynamics

In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string theory, loop quantum gravity, and black-hole physics. We analytically obtain the partition function, probability function, internal energy, and the specific heat capacity of the vibrational quantum system for $1<q<frac{3}{2}$ and compare the results with those of Tsallis and Boltzmann-Gibbs statistics without the minimal length scale.