The physical aging of polystyrene (PS) free-standing films has been investigated as a function of the films thickness, ranging from several 77, I 11 micrometers to tens of nanometers. In this range of thicknesses, unchanged segmental dynamics in comparison to the bulk was previously reported. This study has been carried out through differential scanning calorimetry (DSC), by following the enthalpy recovery to monitor the physical aging process at different temperatures. The temperature marking the onset of nonequilibrium effects, that is the onset of the glass transtion temperature, T-g(on), was also assessed, at different cooling rates. An acceleration of the physical aging process, and consequently a depression of T-g(on), is found with decreasing the films thickness, already for thicknesses in the micrometer range. Moreover, the onset of nonequilibrium effects is shown to be cooling rate dependent, this being more pronounced when the PS films get thinner. The thickness effects on the typical signatures of the out-of-equilibrium dynamics of the films, namely their physical aging and T-g(on), can be well accounted for by assuming an equilibration mechanism based on volume holes diffusion toward the interfaces of the films. The temperature dependence of the diffusion coefficient obtained within this framework is found to crossover from Vogel-Fulcher-Tammann (VFT) to Arrhenius when decreasing the temperature. The implications of these results are discussed.