Theory of Thermopolarization Effect

We study the polarization response to a temperature gradient in insulators, known as the thermopolarization effect. We show that this response can be understood through the free energy response function to an electric field gradient, which we call the Q tensor. By using the Q tensor, we present a unified description of the polarization responses to both electric fields and temperature gradients and derive the generalized Mott relation. Additionally, we draw an analogy with the anomalous Hall and Nernst effects. These effects are observable as the Seebeck effect when the system's linear size is shorter than the screening length.