Maximum or minimum entropy generation for open systems?

Entropy generation is analysed and obtained from the entropy balance for open systems, considering the lifetime of the natural real process. The Lagrangian approach is discussed in order to develop an analytical method to obtain the stationary states of the open irreversible systems. The stationary conditions of the open systems are obtained in relation to the entropy generation and its maximum principle. An analysis of both minimum and maximum entropy generation is proposed, suggesting that they are two different viewpoints of the same aspect: the first is related to the system, while the second is related to the interaction between the system and the environment.