The minimal length uncertainty and the nonextensive thermodynamics

TL;DR

This paper investigates how a minimal length uncertainty influences the thermodynamics of a quantum harmonic oscillator within the Tsallis nonextensive framework, deriving key thermodynamic quantities and comparing them to classical results.

Contribution

It introduces an analytical study of quantum harmonic oscillator thermodynamics incorporating minimal length effects in Tsallis statistics, extending prior models without this scale.

Findings

Derived analytical expressions for partition function, internal energy, and specific heat with minimal length.

Identified differences between Tsallis and Boltzmann-Gibbs thermodynamics in the presence of minimal length.

Compared thermodynamic properties with and without minimal length, highlighting quantum gravity effects.

Abstract

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.