Modified entropies as the origin of generalized uncertainty principles

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