  Starting from a detailed model for the kinetics of a step edge or island
boundary, we derive a Gibbs-Thomson type formula and the associated step
stiffness as a function of the step edge orientation angle, $theta$. Basic
ingredients of the model are: (i) the diffusion of point defects (``adatoms'')
on terraces and along step edges; (ii) the convection of kinks along step
edges; and (iii) constitutive laws that relate adatom fluxes, sources for
kinks, and the kink velocity with densities via a mean-field approach. This
model has a kinetic (nonequilibrium) steady-state solution that corresponds to
epitaxial growth through step flow. The step stiffness, $\tbe(\theta)$, is
determined via perturbations of the kinetic steady state for small edge Peclet
number, P, which is the ratio of the deposition to the diffusive flux along a
step edge. In particular, $\tbe$ is found to satisfy $\tbe =O(\theta^{-1})$ for
$O(P^{1/3}) <\theta \ll 1$, which is in agreement with independent,
equilibrium-based calculations.
