Universal thermopower of bad metals

``Bad metals'' are known to have a large linear resistivity at high $T$ that is universally seen near the Mott-Hubbard insulating phase. Less well known is that the thermopower $\ensuremath{\alpha}(T)$ of the Mott-Hubbard systems also exhibits simple universal features: (i) close to the insulating phase, where the resistivity has a low-temperature upturn, $\ensuremath{\alpha}(T)$ has a pronounced low-$T$ peak that shifts to higher $T$ with doping; (ii) when the resistivity is nearly linear, which occurs at moderate doping, $\ensuremath{\alpha}(T)$ has a small low-$T$ peak that shifts to lower $T$ with doping and has a high-$T$ sign change; and (iii) at the highest doping, where the resistivity acquires a ${T}^{2}$ term, $\ensuremath{\alpha}(T)$ is negative and depends monotonically on $T$. The universality $\ensuremath{\alpha}(T)$ can be understood using the Kelvin formula and the fact that the chemical potential for doped Mott insulators displays similar behavior at high $T$. The universality is illustrated with the exact solution of the simplest model for a doped Mott insulator at high $T$.