Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?

TL;DR

This paper compares the effects of the Modified Uncertainty Principle and polymer quantization on simple quantum systems and their thermodynamics, finding identical results but different theoretical origins.

Contribution

It demonstrates that the thermodynamic predictions of the Modified Uncertainty Principle match those of polymer quantization, highlighting potential conceptual connections.

Findings

Thermodynamic entities are identical in both frameworks.

The length scale has different theoretical origins.

Suggests further investigation into fundamental connections.

Abstract

In this Letter we study the effects of the Modified Uncertainty Principle as proposed in Ali et al. (2009) [5] in simple quantum mechanical systems and study its thermodynamic properties. We have assumed that the quantum particles follow Maxwell-Boltzmann statistics with no spin. We compare our results with the results found in the GUP and polymer quantum mechanical frameworks. Interestingly we find that the corrected thermodynamic entities are exactly same compared to the polymer results but the length scale considered has a theoretically different origin. Hence we express the need of further study for an investigation whether these two approaches are conceptually connected in the fundamental level.