  The thermodynamic second law in the evaporating black hole space-time is
examined in the context of two-dimensional dilaton black hole. The dynamical
evolution of entropy is investigated by using the analytical perturbation
method and the numerical method. It is shown that the thermodynamic second law
holds in the vicinity of infalling shell %analytically and in the region far
from the infalling shell %numerically in the case of semi-classical CGHS model.
The analysis of the general models is also presented and its implication is
discussed.
