*Abstract:* I will discuss examples of deterministic cellular automata that exhibit behavior reminiscent of the second law of thermodynamics: starting from a state with slight randomness, the cellular automaton evolves towards an equilibrium state characterized by maximum randomness. Proofs are known only for models with algebraic structure, although rather strong empirical (simulation) evidence is present for other examples. I will then continue to talk about the"states of macroscopic equilibrium" in reversible cellular automata, presenting some results and open problems.