This chapter derives the balance equation for entropy—a lengthy calculation—which provides for the rate of entropy production per volume. Non-equilibrium thermodynamics is an extension of thermodynamics whereby state variables become field quantities, functions of spatial coordinates and the time. More complex phenomena arise when two or more of these basic effects are present simultaneously. In thermoelectricity, electrical conduction and heat conduction occur together. When a temperature gradient is set up, not only does heat flow but an electric field is created. For multicomponent systems, people need to specify particle numbers on a per-mass basis. To obtain an energy balance equation, one must start with an accounting of momentum: The time rate of change of momentum is a force, and from a force people can obtain the mechanical energy by the work done by forces. To derive the local balance equation for energy, people develop separately balance equations for kinetic and potential energies.