The Wiedemann–Franz law linking electrical and thermal conductance has now been verified experimentally in atomic junctions.
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Kolosov, O. Heat flow in atomic bottlenecks. Nature Nanotech 12, 402–403 (2017). https://doi.org/10.1038/nnano.2016.306
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DOI: https://doi.org/10.1038/nnano.2016.306