The Different Types of Cellular Automata

The question is, has anyone done research in determining the entropy of different states for various cellular automata rule sets? So I think this is a different thing because now we're talking about cellular automata rather than statistical mechanics. The typical cellular automata that people talk about aren't irreversible, even at the microscopic level. You don't need to start in a special state necessarily to see complexity emerge. It's an open question. It depends on the kind of cellular automaton you're working on. And it can evolve into a very high information density state. That can't happen in classical mechanics, but it can happen in cellular automata. so it's just a very different question.