Two- and four-point Kapitza resistance between harmonic solids

The calculation of the Kapitza boundary resistance between dissimilar harmonic solids has since long (Little [Can. J. Phys. 37 (1959) 334]) suffered from a paradox: this resistance erroneously tends to a finite value in the limit of identical solids. We resolve this paradox by calculating temperature differences in the final heat-transporting state, rather than with respect to the initial state of local equilibrium. We thus derive an exact, paradox-free formula for the boundary resistance. We compare the definition of local temperatures in terms of “nonequilibrium” energy densities with the (phase-sensitive) measurement of such a temperature by attaching a probe to the system, and find considerable agreement between the two. The analogy to ballistic electron transport is explained.