Heat can flow without temperature differences - but thermodynamics remains intact.
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References
Das, S., Narayan, O. & Ramaswamy, S. A ratchet for heat transport between identical reservoirs. Preprint, (2002).
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Ball, P. Going against the flow. Nature (2002). https://doi.org/10.1038/news020624-1
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DOI: https://doi.org/10.1038/news020624-1