Explicit construction of steady state of a model of chemical turbulence

Using only the microscopic dynamics, the nonequilibrium steady state of a one-dimensional cellular automaton (CA) model of chemical turbulence is explicitly constructed. A coding is found which decomposes the CA into three interacting shift systems, each of which has an independent steady-state distribution. It was previously shown that the steady state of this model is a Gibbs state. Hence the steady state can be represented in the form Z^-1e^-F, where F is the "conditional energy" of the system such that all conditional probabilities are continuous. It is shown that the conditional energy of this model has an approximate expression in terms of familiar models from equilibrium statistical mechanics.