Conway's Game of Life is clearly non-reversible, right? So enthropy must go up; information must be steadily lost, and it certainly can't go up.
Let us consider the amount of information in an initial configuration. To do that, we must certainly restrict the initial configuration's size. This does not seem to be an important issue, because in all (few) cases I've seen the initial configuration was confined to a small part of the board, usually less that 10 x 10. Then it is easy to calculate the information, which will depend exclusively on the allowable initial size and the initial configuration symmetries (we must indentify the configurations that are related to each other by mirror, rotational, or shift symmetry).
Now, some of these initial configurations evolve to very complicated, expanding configurations. It would seem that to describe these, more information is necessary. Since the game is irreversible, we can't shrink the description by tracing back to the initial configuration. Where is the catch?