Recently, there has been a lot of talk in the media about the "Big Rip". It most certainly resulted from the paper by Marcelo M. Disconzi and Thomas W. Kephart where they have figured out a mathematical system that allows the state parameter of the vacuum energy to drop below -1. Obviously this means the big rip is a possibility (perhaps a certainty?) and they have calculated the time frame to be 22 billion years. My question is what happens to the Poincaré recurrence theorem in a big rip universe? Is it still a possibility? And if yes then does the big rip lead us back to the classic Boltzmann brain situation?