We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identiﬁed by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the ﬁrst law of quantum dynamical horizon in terms of a ﬂuctuation-dissipation relation applied to this fundamental discrete structure. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. We investigate the ﬁnal stage of the evaporation process and show how the dynamics leads to the formation of a massive remnant. Implications for the information paradox are discussed.