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 < 32 and compare the results with those of Tsallis and Boltzmann-Gibbs statistics without the minimal length scale.

Minimal length · Generalized uncertainty principle · Nonextensive thermodynamics