where ∇ ∇ T is the temperature gradient, and K is the Thomson coefficient. The Thomson effect is a manifestation of the direction of flow of electrical carriers with respect to a temperature gradient within a conductor. These absorb energy (heat) flowing in a direction opposite to a thermal gradient, increasing their potential energy, and, when flowing in the same direction as a thermal gradient, they liberate heat, decreasing their potential energy. The Thomson coefficient is related to the Seebeck coefficient as K = T d S d T (see below). This equation, however, neglects Joule heating and ordinary thermal conductivity (see full equations below).