Validity of Prigogine’ s minimum entropy production principle for a rigid heat-conducting solid beyond the Fourier heat transport regime

The question of the validity of Prigogine’ s minimum entropy principle (MEPP) for the stationary state in the case of heat transport in a rigid solid is addressed. While the well-known condition of a constant phenomenological coefficient in the usual linear law of classical irreversible thermodynamics relating the heat flux and the temperature gradient is a sufficient requirement to guarantee the validity of the MEPP, it has the major drawback that no existing real material fulfills such condition. A less restrictive condition in which Fourier’s law is no longer obeyed and the phenomenological coefficient is independent of temperature but depends on position (which for instance may happen in solids with internal structure or in alloys with an inhomogeneous distribution of mass) is considered and shown to be at grips with the MEPP for the stationary state, thus extending its range of validity. A possible physical realization based on a SiGe alloy is examined, and the stationary temperature profiles corresponding to the minimum global entropy production are obtained.