We derive the thermodynamic limits of harvesting power from the outgoing thermal radiation from the ambient to the cold outer space. The derivations are based on a duality relation between thermal engines that harvest solar radiation and those that harvest outgoing thermal radiation. In particular, we derive the ultimate limit for harvesting outgoing thermal radiation, which is analogous to the Landsberg limit for solar energy harvesting, and show that the ultimate limit far exceeds what was previously thought to be possible. As an extension of our work, we also derive the ultimate limit of efficiency of thermophotovoltaic systems.
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