Basically I'm curious as to whether or not sleep loss or gain is purely additive. I'm not sure if this is even the right way to phrase this question, so I'll give an example. Say someone stays up to 3AM every day for a week. If they then get one or two days of normal rest (8-9 hours, say) will they be mostly functional again? Or would their bodies need to gain back all of the hours (likely through a day or two of a LOT of sleep), to flush out all of the toxins that have built up in their brain from staying up? (I have a very loose understanding of the importance of sleep.)
To summarize, after pulling many [close-to-]all-nighters, would a day of 15-hours of sleep be any more rejuvenating than a normal night of sleep, and why?