<John: Poincaré's Recurrence Theorem says any dynamical system composed of a finite number of particles (as the human brain is) will, given sufficient time, return to its original state, however I wouldn't consider just repeating the same identical thing over and over again to be an afterlife because repeating an event an infinite number of times and doing it just once would be subjectively identical. And subjectivity is the most important thing in the universe, or at least it is in my subjective opinion. But if you could keep on increasing the number of particles, that is to say if your brain kept getting bigger, then you could keep on having novel experiences until you ran out of particles to add. >
Poincaré’s eternal return universe would be a repetitive closed loop without novelty as you say. It would be a loop because in classical mechanics different phase space paths don’t intersect (if they did, one present would have multiple futures), so if two paths intersect once they are one and the same path.
Palmer says that the universe will return to a state that is arbitrarily close (not identical) to any previous state. In his theory, inspired by fractal and chaos maths, the universe will eventually (after a loooong time) return to a state very close (arbitrarily close) to its current state. And then again and again on new paths in the fractal invariant set.
But there are variations, and then other variations ever and ever again, so it is not the same one life over and over, and there are real subjective experiences forever. And you keep meeting new versions of your loved ones forever! To me, this is an emotionally satisfying concept of afterlife.