Modified entropies as the origin of generalized uncertainty principles

TL;DR

This paper demonstrates that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, suggesting a link between quantum gravity effects and non-extensive statistical frameworks.

Contribution

It introduces a novel derivation of GUP from non-extensive entropies, expanding the understanding of quantum gravity signatures.

Findings

Deformation parameters for $S_{+}$ and $S_-$ entropies are negative and positive.

Non-extensive statistics serve as a signature of quantum gravity.

GUP can be connected to non-extensive entropy frameworks.

Abstract

The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with $S_{+}$ and $S_-$ entropies are negative and positive respectively. This allows us to explore various possibilities in the search of physical implications. We conclude that non-extensive statistics constitutes a signature of quantum gravity.