As mentioned earlier, class 4 cellular automata are distinguished by the presence of simulation paths leading to every other cellular automaton rule. It is likely that no specific path is distinguished as attractive. Cellular automata of different classes may thus be distinguished by their limiting behavior under simulation transformations. This approach suggests that classification of the qualitative behavior of cellular automata may be related to determinations of equivalence of systems and problem classes in computation theory. In general, one may hope for fundamental connections between computation theory and the theory of complex nonequilibrium statistical systems.
Information theory forms a mathematical basis for equilibrium statistical mechanics.
Computation theory, which addresses time-dependent processes, may be expected to play a fundamental role in nonequilibrium statistical mechanics.