Through time-dependent gas transport properties, we have investigated the physical aging process of amorphous glassy polymer films made from a polynorbornene. By combining the concepts of free volume and the kinetic theory of glass stabilization, it was found that the time dependence of the gas permeability could be rationalized through the thickness dependence of the glass transition temperature. A mathematical relationship was developed that directly relates polymer physical aging (tracked by the gas permeability decay) and sample thickness. It was confirmed by permeation measurements with nitrogen and helium that the aging process is accelerated for thin glassy polymer films (about 8000 Angstrom). The theoretical results show that accelerated aging for thin films compared to thick films can be qualitatively predicted, based on the decrease in the glass transition temperature when the film thickness decreases.