The physical defects of the hyperbolic heat conduction equation

With the advent of lasers with ultrashort pulse duration (ps, fs) for use in materials processing, the question of the validity of the conventional heat conduction theory arises. It is often claimed that at very short timescales the effect of thermal wave propagation becomes important and must be included via the so-called hyperbolic heat conduction equation (HHCE). The HHCE is a damped wave equation where thermal waves travel back and forth at a finite propagation speed. In this paper the HHCE is inspected on a microscopic level from a physical point of view. Starting from the Boltzmann transport equations we study the underlying approximations. We find that the hyperbolic approach to the heat current density violates the fundamental law of energy conservation. As a consequence, the HHCE predicts physically impossible solutions with a negative local heat content. This behaviour is demonstrated in detail for a standard problem in heat conduction, the solution for a point source.