Local versus nonlocal constitutive theories of nonequilibrium thermodynamics: the Guyer–Krumhansl equation as an example

On the example of the celebrated Grad’s 13-moment system of kinetic theory of rarefied gases and phonon hydrodynamics, it is proved that the constitutive equations of nonequilibrium thermodynamics must be nonlocal. A thermodynamic model of Guyer–Krumhansl heat-transport equation is derived within the frame of weakly nonlocal Rational Thermodynamics. The constitutive equation for the entropy flux is analyzed as well. Some nonlinear generalizations of Maxwell–Cattaneo equation are studied in view of the experiments on thermal wave propagation.