One can see a one-to-one correspondence between the electrostatic and thermal quantities: Temperature T(<b>r</b>) is analogous to the electric scalar potential Φ(<b>r</b>), the volume heat source density w(<b>r</b>) is analogous to the volume charge density ρ(<b>r</b>), and the thermal conductivity k is analogous to the permittivity ε.
Similarly, one can establish an analogy between the heat flux <b>q(r)</b> and the static electric field <b>E(r)</b>:
<math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r})</math>
{| class="wikitable"