It is well known that volume diffusivity in nanocrystalline materials is orders of magnitude greater than that in coarse grained materials of identical chemistry. The present study offers a theoretical explanation of this enhancement by attempting to correlate the diffusivity with the excess free volume of the grain boundary atoms in the nanocrystalline materials. Assuming a simplified geometry of the nanocrystalline aggregate, the excess free volume of the grain boundary atoms has been expressed as a function of grain size. Applying the concept of isothermal equation of state, it is shown that the effect of negative hydrostatic pressure on the diffusion kinetics in nanocrystalline materials at a given temperature is equivalent to the same obtained for coarse grained materials at an effective elevated temperature. The predicted results have been compared with the earlier published relevant experimental data from several Cu-based systems.