A critical analysis of the minimum entropy production theorem and its application to heat and fluid flow

We discuss the principle of minimum entropy production as proposed by Prigogine, providing two examples (heat conduction in a fluid at rest and the combined shear flow and heat conduction in an incompressible fluid) for which the principle produces field equations that do not agree with the balance equations of continuum mechanics. We have not been able to find any special assumption on the temperature dependence on the phenomenological coefficients (such as thermal conductivity and dynamical viscosity) under which a general agreement between standard balance equations and balance equations determined by the minimum entropy production principle can be stated. A critical analysis of the theorem proof shows that the minimum entropy production of system in a stationary state cannot be different from zero.