  We present a mesoscopic model for thermoelectric phenomena in terms of an
interacting particle system, a lattice electron gas dynamics that is a suitable
extension of the standard simple exclusion process. We concentrate on
electronic heat and charge transport in different but connected metallic
substances. The electrons hop between energy-cells located alongside the
spatial extension of the metal wire. When changing energy level, the system
exchanges energy with the environment. At equilibrium the distribution
satisfies the Fermi-Dirac occupation-law. Installing different temperatures at
two connections induces an electromotive force (Seebeck effect) and upon
forcing an electric current, an additional heat flow is produced at the
junctions (Peltier heat). We derive the linear response behavior relating the
Seebeck and Peltier coefficients as an application of Onsager reciprocity. We
also indicate the higher order corrections. The entropy production is
characterized as the anti-symmetric part under time-reversal of the space-time
Lagrangian.
