It isn’t true that irreversibility per se implies an increase of entropy—or at least I can’t see how it follows from the definition. (And couldn’t there be a universe whose ‘laws of physics’ were such that states may have multiple successors but at most one predecessor—so that by the ‘irreversibility’ criterion, entropy is decreasing—but which had a ‘low entropy’ beginning like a Big Bang and consequently saw entropy increase over time?)
In any case, it’s not clear (to me at least) how the definition of entropy applies to the Game of Life.
It isn’t true that irreversibility per se implies an increase of entropy—or at least I can’t see how it follows from the definition. (And couldn’t there be a universe whose ‘laws of physics’ were such that states may have multiple successors but at most one predecessor—so that by the ‘irreversibility’ criterion, entropy is decreasing—but which had a ‘low entropy’ beginning like a Big Bang and consequently saw entropy increase over time?)
In any case, it’s not clear (to me at least) how the definition of entropy applies to the Game of Life.