Use and validity of principles of extremum of entropy production in the study of complex systems

• The principles of extremum of entropy production are not first principles.
• They result from the maximization of conductivities under appropriate constraints.
• The conditions of their validity are set explicitly.
• Some long-standing controversies are discussed and clarified.

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented.