On the principle of minimal entropy production for Navier-Stokes-Fourier fluids

In this paper we discuss the principle of minimal entropy production, proposed by Prigogine [1], which affirms that the global entropy production approaches a minimum as a process becomes stationary.

We point out in two particular cases that this principle produces field equations that do not agree with the equations of balance of mass, momentum and energy. The processes considered are:

• heat conduction in a fluid at rest

• shear flow and heat conduction in an incompressible fluid.

Now is the appropriate time to review Prigogine's principle, since in recent years a new, $-$ and different $-$ principle of minimal entropy production has been proposed. This is the “minimax principle” postulated by Struchtrup & Weiss [2]. Within the context of extended thermodynamics this new principle shows great promise.