For the HHC equation to remain compatible with the first law of thermodynamics, it is necessary to modify the definition of heat flux vector, q, to τ τ 0 ∂ ∂ q ∂ ∂ t + q = − − k ∇ ∇ θ θ , where τ τ 0 is a relaxation time, such that C 2 = α α / τ τ 0 . This equation for the heat flux is often referred to as "Maxwell-Cattaneo equation". The most important implication of the hyperbolic equation is that by switching from a parabolic (dissipative) to a hyperbolic (includes a conservative term) partial differential equation, there is the possibility of phenomena such as thermal resonance and thermal shock waves.