I speak as someone who has fasted up to 1 week. Interestingly, the difficult period is exactly the initial 2...3 days. After that it's no effort at all - albeit physical performance seems to decrease, of course.
The human body could go on like that for a few weeks actually, but I don't think there are any benefits beyond 2...3...4 days [research needed], and the dangers multiply rapidly the more you push into very long durations.
Also as others have said it, you go over a bump and it becomes easy. Also, there is a window where I'm rather productive and less ADD when I'm fasting.
Something happens to the brain during prolonged fasting (within reason), and it's something that seems pretty darn good overall.
If you practice meditation, fasting seems to help a lot.
The research was also summarized as "always gamble on an empty stomach."
The published paper: http://www.cell.com/cell-stem-cell/abstract/S1934-5909(14)00...