Abstract
In this paper we propose a solution to the problem associated with the presence of an incomplete differential of entropy in Prigogine's theorem on the minimum of entropy production. A generalized theorem on the minimum rate of change of entropy near the stationary state of the system, which is under the influence of the entrostat, is formulated. It is shown that the mathematical expression of the generalized theorem contains the full differential of entropy. •Our new method consists in applying of the statistical criterion for the entropy change in an open system (SCEC) for analyzing the I.•Prigogine's model in order to generalize the theorem on the minimum entropy production for the case of the total differential of entropy.