Modified entropies as the origin of generalized uncertainty principles

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.

arXiv admin note: text overlap with arXiv:hep-th/0305262, arXiv:hep-ph/0308138 by other authors

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• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Semiclassical resolution of the black hole singularity inspired in the minimal uncertainty approach
• On the algebraic approach to GUP in anisotropic space
• GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
• Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach
• Energy-time uncertainty relation from entropy measures