Operation Phoenix is a plan from John William Grant aka J, Daniel McLaughlin, Kira to save humanity. The plan is to gather the name from most psychopaths that there are, and then finally kill all of them in one day. The plan's to mulitate humanity so much, that they don't know but to become peaceful to each other, since most psychopaths are dead, and the whole humanity saw how they died, they were scared, afraid of being killed, afraid of being judged, but then they changed. The enviroment changed, the humans weren't surrounded by psychopaths, liars and corrupt people, they had no other choice but to change for the better.
This operaion also involved Johns death, which he himself planned as a punishment for the genocide he'd commit. He writes his name into the notebook making himself die 23 days after the genocide. Elizabeth dies 23 days later too, since she writes her name in the notebook too, since she thinks that she also deserves being punished.