  A local equilibrium approach for the kinetics of a simplified protein folding
model, whose equilibrium thermodynamics is exactly solvable, was developed in
[M. Zamparo and A. Pelizzola, Phys. Rev. Lett. 97, 068106 (2006)]. Important
properties of this approach are (i) the free energy decreases with time, (ii)
the exact equilibrium is recovered in the infinite time limit, (iii) the
equilibration rate is an upper bound of the exact one and (iv) computational
complexity is polynomial in the number of variables. Moreover, (v) this method
is equivalent to another approximate approach to the kinetics: the path
probability method. In this paper we give detailed rigorous proofs for the
above results.
