Spatial distribution of Joule heat in nanostructures

The Joule heat generation in a quantum semiconductor nanowire joining two classical reservoirs is considered. We assume that the conductance of the system is determined by the phonon-assisted ballistic resistance. The spatial distribution of the generated heat is analysed. The heat generated within the nanostructure is determined. It is simply related to the phonon-assisted variation ΔG of the conductance. For a fixed voltage, the corresponding variation of the overall heat generation is negative and is determined by ΔG. Due to the same interaction the reduction of the heat generated in each reservoir is the same as the heat generated in the nanostructure. In other words, the presence of collisions within a nanowire does not violate the equality of the heat release in the reservoirs that are connected by the nanowire, although the rates and mechanisms of relaxation there may be different. We come to the conclusion that further investigation of various situations where the nanostructures are involved is needed to gain understanding as to why in some cases different heat generation in the two reservoirs is observed and predicted.