Modified entropies as the origin of generalized uncertainty principles

• URL: http://arxiv.org/abs/2206.14166v2
• Date: Thu, 29 Dec 2022 04:46:43 GMT
• Title: Modified entropies as the origin of generalized uncertainty principles
• Authors: Nana Cabo Bizet, Octavio Obreg\'on and Wilfredo Yupanqui
• Abstract summary: Heisenberg uncertainty principle is connected to the entropic uncertainty principle. Due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP)
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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