Several recent simulation and experimental studies have explored the effects of deformation on the dynamics of glassy materials, and both have demonstrated that the segmental dynamics in glassy polymers can be enhanced by up to two orders of magnitude. However, the origins of the enhanced dynamics remain largely unknown. Furthermore, it is not known how the observed changes are affected by aging processes. In this study, we have performed extensive molecular dynamics simulations of a pure polymer glass and a polymer nanocomposite glass under stress in the nonlinear creep regime. We measure the dynamics using the bond autocorrelation function and show that the effective relaxation times are reduced during the deformation by up to two orders of magnitude. The dynamics are most enhanced during periods of high strain rate, and we also find the largest changes in the features of the potential energy landscape during periods of fast dynamics and high strain rate. Additionally, we find that the relaxation times in the nanocomposite have approximately the same dependence on strain rate as the pure polymer at a constant temperature despite being farther into the glassy state. The results of our simulations are compared to those of fluorescence recovery after photobleaching. The agreement between theory and experiment is highly satisfactory, giving credence to the conclusions extracted from our molecular simulations.