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</b>(<b>r)</b> ) and the static electric field <b>E</b>(<b>r)</b>):
<math> q(\mathbf{q(r}) } = -k\nabla T(\mathbf{r}) \quad \leftrightarrow \quad \mathbf{E(r)} = - \nabla \Phi(\mathbf{r})</math>