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In this paper, we study the thermodynamics of quantum harmonic oscillator inthe Tsallis framework and in the presence of a minimal length uncertainty. Theexistence of the minimal length is motivated by various theories such as stringtheory, loop quantum gravity, and black-hole physics. We analytically obtainthe partition function, probability function, internal energy, and the specificheat capacity of the vibrational quantum system for $1<q<\frac{3}{2}$ andcompare the results with those of Tsallis and Boltzmann-Gibbs statisticswithout the minimal length scale.

The minimal length uncertainty and the nonextensive thermodynamics