  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.
