  We prove the Jonson-Mahan theorem for the thermopower of the Falicov-Kimball
model by solving explicitly for the correlation functions in the large
dimensional limit. We prove a similar result for the thermal conductivity. We
separate the results for thermal transport into the pieces of the heat current
that arise from the kinetic energy and those that arise from the potential
energy. Our method of proof is specific to the Falicov-Kimball model, but
illustrates the near cancellations between the kinetic-energy and
potential-energy pieces of the heat current implied by the Jonson-Mahan
theorem.
