Uncertainty Principles and Maximum Entropic Force

Abstract

We consider quantum gravity corrections to the maximum entropic force that arise from several gravitational uncertainty principles. These include the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), the Generalized Extended Uncertainty Principle (GEUP), and the Linear-Quadratic GUP (LQGUP). We find that the modified entropic force depends on the dimensionless parameters of the uncertainty principles and, thus, on the underlying quantum gravity theory. Furthermore, the entropic force, which is quantum gravity corrected in the framework of the extended uncertainty principles, also depends on the number of Planck areas that made the ``EUP area".