Comment on entropy in two-dimensional dilaton gravity

The thermodynamic second law in the evaporating black hole space-time is examined in the context of the 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 and in the region far from the infalling shell in the case of the semi-classical CGHS model. The analysis of general models is also presented and its implication is discussed.