We determine the adsorption rate of polymer melts by means of measurements of molecular mobility. We show that the complex set of molecular rearrangements involved in the adsorption of polymers on flat surfaces can be modeled as an equilibration kinetics driven by the slow Arrhenius process (SAP), a recently discovered molecular mechanism. Our predictive model is based on the single hypothesis that the number of chains adsorbed per unit surface within the timescale of spontaneous fluctuations associated to the SAP is a temperature-invariant constant, not depending on the chemical structure of the polymer. Going beyond the qualitative arguments setting a correlation between equilibrium and nonequilibrium properties, we demonstrate that the rate at which an adsorbed layer grows does not depend on interfacial interactions. By considering simple physical arguments, we demonstrate that this quantity can be straightforwardly determined using the energy barrier of molecular motion as only input.