The effects of low energy plasma processing on the morphological evolution of copper thin films is examined using atomic force microscopy. It is shown that there appears to be a coupling between the shape evolution of the surface morphology of the thin film to the grain size evolution within the internal microstructure of the film. A linear perturbation model based on localized changes in grain boundary curvature due to preferential grain boundary grooving, is developed to couple the microstructural stability of thin films to dynamic effects due to processing parameters. It is suggested that prior grain size gradients existing in the as-deposited nature of the film have a significant effect on the grain size stability based on flow by mean curvature concepts. Based on this approach, a theoretical framework using the formalism of Fokker-Planck equations, to relate the stochastic nature of atomistic processes Such as plasma processing to the physics of grain growth are also proposed.