I am trying to define a maxwell's demon in the cellular automata world
Maxwell's demon is a thought experiment in thermodynamics to suggest how the second law of thermodynamics can be violated.
As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics.
A demon simply calculates a parameter of the system (velocity of a molecule for the gas box). A cellular world with an array of cells in the middle (somewhere) whose rules are different from the general rule followed by the rest of the cells can be considered as a demon. It takes the last iteration of the general rule as its input for the demon rule and then outputs a new pattern to the general rule.