Crossed nonlocal effects and breakdown of the Onsager symmetry relation in a thermodynamic description of thermoelectricity

Nonlocal nonlinear effects coupling the heat flux and the electric-current density in an enlarged thermodynamic description of thermoelectric systems are considered. The influence of such terms on the breakdown of the Onsager reciprocity relation between the effective transport coefficients, depending on the electric field and the temperature gradient, is analyzed up to second-order in the thermodynamic forces. The maximum value of the thermoelectric efficiency is derived as a function of the figure-of-merit and of the degree of the Onsager symmetry breaking.