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

References in corpus (8)

• Superstatistics, thermodynamics, and fluctuations
• Superstatistical distributions from a maximum entropy principle
• Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?
• Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• Optimal uncertainty relations in a modified Heisenberg algebra
• On superstatistics and black hole quasinormal modes
• On how generalised entropies without parameters impact information optimisation processes

Cited by in corpus (6)

• 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