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Temperature relaxation and the Kapitza boundary resistance paradox

Alec Maassen van den Brink·H. Dekker
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Abstract

The 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.

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Alec Maassen van den Brink, H. Dekker. 1994-07-28. Temperature relaxation and the Kapitza boundary resistance paradox. https://arxiv.org/abs/cond-mat/9407113

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