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Yeah this is all rather confusing...

This boils down to a moderately heated BB receiving an large stream of moderately powered photons and either rejecting them or first absorbing and then radiating them away at the same pace without changing its own temperature, regardless of how many photons are coming in.

Yeah I don't see how this argument holds water at all. If you have 10 kW worth of photons focused onto a square inch that absorbs 90% of those photons then that's 9 kW of power that isn't just going to magically disappear and it's not going to reach equilibrium until it's emitting 9 kW of power itself which is certainly going to be thousands of degrees. While the entropy argument is certainly an interesting thought experiment all that means is that the global entropy must somehow still be increasing.

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