Generalized uncertainty principle and quantum gravitational friction

The Generalized Uncertainty Principle gives place to deformed commutation relations which are linear or quadratic in particle momenta. In this article we show that, in the linear case, which corresponds to double special relativity theories, this deformation is equivalent to a gravitationally-induced damping process in an Ohmic environment at zero temperature. Therefore, both minimum length and maximum momentum give place to quantum gravitational friction.