Thanks everyone for the feedback.
I'm not sure if the eternal recurrence card is as OP as people might think.
Regarding the duration, I called the card eternal recurrence because I wanted it to be eternal. (Of course, a simple deflag will eliminate the permanent as would pulverizer like any permanent. There seems to be no reason to steal the card though.)
I'm not sure how much it would change the metagame in some respects. There are plenty of ways to control creatures without killing them, for example freezing, congealing, basilik blood. So it might place greater emphasis on using those kinds of cards when you are confronted with eternal recurrence. A permafrost shield is an excellent non-lethal way of reducing exposure also or other non-lethal shield.
Obviously devouring would be much less important in a round with an eternal recurrence, but of course, you could build up an oty by devouring your own creatures and recasting them if you thought that was effective.
Since it is global, it benefits both players meaning that it is a plus and a minus. It could allow players to build decks using fewer creatures under the assumption they could recast the ones they had if they died.
I've also been playing around with a rainbowed mummy/eternity deck using 7 quanta pillars and 6 supernovas. (Time/Death mix) It takes a long time to get enough time quantas up to get the eternity out, cast the rewind on the mummy and then even longer to get a scarab into play. Time seems quite hard to come by in rainbow decks. (Though not as hard as entropy). A 12 time casting cost is pretty high in a rainbow deck. If you went with a time deck or time mixed deck, that would obviously be easier to meet.
Logistically, it appears that the most that would be possible would be a mixed fill your hand with as many as you can and rest to deck. The limit on cards appears to be 8... If you exceeded the 8 card in hand limit somehow and did not have the quanta to cast, you would have to discard the cards (this would be interesting as well).
The cards could also all go back to the deck, but everyone knows that can be very problematic, because you can't get to your other cards then. Might want an hourglass then.
I'm glad the card is seen as changing the game a bit, since otherwise, what would be the point of the suggestion?
To really understand the effects of the card it would have to be tested. I certainly think the cards are worth testing.