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.

Automated summary

The study shows that the constitutive equations of nonequilibrium thermodynamics must be nonlocal. A thermodynamic model of the Guyer-Krumhansl heat-transport equation is derived within the framework of weakly nonlocal Rational Thermodynamics. Additionally, some nonlinear generalizations of the Maxwell-Cattaneo equation were studied in the context of experiments on thermal wave propagation.