Recently, in theoretical biology and in biophysical engineering the entropy production has been verified to approach asymptotically its maximum rate, by using the probability of individual elementary modes distributed in accordance with the Boltzmann distribution. The basis of this approach is the hypothesis that the entropy production rate is maximum at the stationary state. In the present work, this hypothesis is explained and motivated, starting from the entropy generation analysis. This latter quantity is obtained from the entropy balance for open systems considering the lifetime of the natural real process. The Lagrangian formalism is introduced in order to develop an analytical approach to the thermodynamic analysis of the open irreversible systems. The stationary conditions of the open systems are thus obtained in relation to the entropy generation and the least action principle. Consequently, the considered hypothesis is analytically proved and it represents an original basic approach in theoretical and mathematical biology and also in biophysical engineering. It is worth remarking that the present results show that entropy generation not only increases but increases as fast as possible. © Copyright EPLA, 2013.
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