Thermal and electrical transport formalism for electronic microstructures with many terminals

The Landauer-Buttiker formalism for an electronic microstructure with many terminals is extended to account for temperature changes in the reservoirs and heat fluxes in the terminals. Terminal relations are developed in the presence of an arbitrary applied magnetic induction field which becomes uniform in the neighborhood of each terminal. They use temperature changes in the reservoirs and either chemical potential changes in the reservoirs or charge fluxes in the terminals as independent variables. In both cases formulae for the transport matrices are given in terms of the scattering matrix of the microstructure. Onsager symmetry relations and reciprocity theorems are given for electrical, thermal and thermoelectric configurations. The behaviour of quantum point contacts is outlined.