In the absence of matter flows, Fourier's law is usually written: J u = − − k ∇ ∇ T ; where k is the thermal conductivity. However, this law is just a linear approximation, and holds only for the case where ∇ ∇ T ≪ ≪ T , with the thermal conductivity possibly being a function of the thermodynamic state variables, but not their gradients or time rate of change. Assuming that this is the case, Fourier's law may just as well be written: J u = k T 2 ∇ ∇ 1 T ;