Boltzmann brain is an interesting concept offered initially in response to one of Ludwig Boltzmann’s explanation for the low-entropy state of the Universe. He hypothesized that even a fully random universe would fluctuate towards lower-entropy states. The issue is that many phenomena such as evolved life on Earth are so far from equilibrium it looks like they were extremely unlikely to have happened. In particular, it is much more likely that a single brain would emerge out of the void from random fluctuations than the present state of Earth in terms of distance to equilibrium.
This question of going against equilibrium is interesting and poses some deep questions about the evolution of life on Earth. One obvious objection that comes to mind when relating this to complexity measures and studies of emergence is the fact that simple distance to equilibrium is not a sufficient measure of the complexity of a system and the number of paths leading to this state is also meaningful. Emergence of complexity is happening constantly, but the only tiny fraction of it that is conserved does it because it builds on smaller stable components that it will keep building on (see (Simon 1962)). In the brain vs. humans example, humans where probably more likely to appear because given the local conditions on Earth enabling Evolution, higher complexity was bound to emerge. On the other hand, a single brain popping from the void is a an event that could only result from pure luck and the miraculous alignment of infinitely many unlikely events.
Another thing related to the study of Cellular automata and Evolution is the fact that right now we are more or less searching for a Boltzmann brain inside automata by just sampling them and letting them run. The key is probably, in a similar fashion than humans aren’t a Boltzmann brain, to create the conditions for complexity to keep increasing without being subjected to random fluctuations of the universe.