There is a fundamental quantum limit to heat flow, just as there is to electric current. This limit is independent of what carries the heat, and could also have a role in an unexpected quarter: information theory.
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Schwab, K. Information on heat. Nature 444, 161–162 (2006). https://doi.org/10.1038/444161a
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DOI: https://doi.org/10.1038/444161a
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