Nonequilibrium distribution function in the presence of a heat flux at the interface between two crystals

A one-dimensional harmonic chain model is used to study the non-equilibrium distribution function of phonons induced by a heat flux across the interface between two crystals. Conditions are derived which govern the matching of distribution functions on both sides of the interface. A generalization of the Enskog–Chapman method for calculating the Kapitza conductance is introduced. A precise relation is obtained under some simplifications. This version contains improved translation, modernized notation, and corrects one mistake, that does not affect the final formulae.