Convergence to equilibrium in a class of interacting particle systems evolving in discrete time - art. no. 016117

We conjecture that for a wide class of interacting particle systems evolvin g in discrete time, namely, conservative cellular automata with piecewise l inear flow diagrams, relaxation to the limit set follows the same power law at critical points. We further describe the structure of the limit sets of such systems as unions of shifts of finite type. Relaxation to the equilib rium resembles ballistic annihilation, with "defects" propagating in opposi te directions annihilating upon collision.