to diffuse in. The combination of diffusion and dissipation favours an overall drift of the charge carriers towards the side of the material where they have a lower chemical potential. For the thermoelectric effect, now, consider the case of uniform voltage (uniform chemical potential) with a temperature gradient. In this case, at the hotter side of the material there is more variation in the energies of the charge carriers, compared to the colder side. This means that high energy levels have a higher carrier occupation per state on the hotter side, but also the hotter side has a lower occupation per state at lower energy levels. As before, the high-energy carriers diffuse away from the hot end, and produce entropy by drifting towards the cold end of the device. However, there is a competing process: at the same time low-energy carriers are drawn back towards the hot end of the device. Though these processes both generate entropy, they work against each other in terms of charge current, and so a net current only occurs if one of these drifts is stronger than the other. The net current is given by , where (as shown below) the thermoelectric coefficient depends literally on how conductive high-energy carriers are, compared to low-energy carriers. The distinction may be due to a difference in rate of scattering, a difference in speeds, a difference in density of states, or a combination of these effects. Mott formula The processes described above apply in materials where each charge carrier sees an essentially static environment so that its motion can be described independently from other carriers, and independent of other dynamics (such as phonons). In particular, in electronic materials with weak electron-electron interactions, weak electron-phonon interactions, etc. it can be shown in general that the linear response conductance is and the linear response thermoelectric coefficient is where is the energy-dependent conductivity, and is the Fermi–Dirac distribution function. These equations are known as the Mott relations, of Sir Nevill Francis Mott. The derivative is a function peaked around the chemical potential (Fermi level) with a width of approximately . The energy-dependent conductivity (a quantity that cannot actually be directly measured — one only measures ) is calculated as where is the electron diffusion constant and is the electronic density of states (in general, both are functions of energy). In materials with strong interactions, none of the above equations can be