We present a precise microscopic description of the limiting step for low-t
emperature shape relaxation of two-dimensional islands in which activated d
iffusion of particles along the boundary is the only mechanism of transport
allowed. In particular, we are able to explain why the system is driven ir
reversibly towards equilibrium. Based on this description, we present a sch
eme for calculating the duration of the limiting step at each stage of the
relaxation process. Finally, we calculate numerically the total relaxation
time as predicted by our results and compare it with simulations of the rel
axation process.