Integral equations versus internal variables in the search for an effectively hyperbolic thermal transport equation

To obtain a thermal wave equation predicting finite phase velocity in the infinite‐frequency limit Grad’s 13‐moment method and extended thermodynamics have added a term linear in the time derivative of the heat flux to Fourier’s law. When nonlocal effects are added via a term linear in the heat flux Laplacian, the problem of nonhyperbolicity and infinite phase velocity recurs. One approach postulates an infinite hierarchy of coupled equations, each of which describes time evolution of a flux appearing in the preceding hierarchy equation. This is shown to disagree in the high‐frequency limit with an evolution equation derived by projection operators from the Liouville equation, in which memory and nonlocal effects are represented by integrals over time and space. Nonlocal effects disappear in the infinite‐frequency limit of the latter, but not of the former.