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arXiv · 2206.14166

Modified entropies as the origin of generalized uncertainty principles

Nana Cabo Bizet·Octavio Obregón·Wilfredo Yupanqui
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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.

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Nana Cabo Bizet, Octavio Obregón, Wilfredo Yupanqui. 2022-06-28. Modified entropies as the origin of generalized uncertainty principles. https://doi.org/10.1016/j.physletb.2022.137636

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