2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27145The calculation of the Kapitza boundary resistance between dissimilar harmonic solids has since long (Little [Can. J. Phys. 37, 334 (1959)]) 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. For a one-dimensional model we thus derive an exact, paradox-free formula for the boundary resistance. The analogy to ballistic electron transport is explained.10 p., REVTeX 3.0 with LaTeX 2.09, ITFA-94-24Condensed Mattertext