On the causality requirement for diffusive-hyperbolic systems in nonequilibrium thermodynamics

The classical Newtonian mechanics does not imply any limit for the speeds of propagation of thermomechanical disturbances. However, the physicists firmly believe that the differential equations of nature should exclude instan-taneous propagation and, therefore, they should be cast in the hyperbolic form. Yet, some equations of classical continuum mechanics and thermody-namics, those of Navier-Stokes and Fourier, are parabolic. Such an incom-patibility has prompted a new thermodynamic theory, developed by several authors in the last two decades, the extended irreversible thermodynam-ics, [1, 2, 3]. In such a theory the instantaneous propagation is removed by changing in a subtle way many tenets of classical irreversible thermody-namics. Moreover, some of its basic postulates are inspired by the kinetic theory of gases. Such an approach seems to be questionable to those sci-entists who, along with Truesdell, believe and claim that in a macroscopic framework ”not even the form of the constitutive equations is derived from the molecular theory, rather the molecular theory so called is forced int