Predictive Information in a Nonequilibrium Critical Model

We propose predictive information, that is, information between a long past of duration T and the entire infinitely long future of a time series, as a general order parameter to study phase transitions in physical systems independently of the underlying dynamics. It can be used, in particular, to study nonequilibrium transitions and other exotic transitions, where a simpler order parameter cannot be identified using traditional symmetry arguments. As an example, we calculate predictive information for a stochastic nonequilibrium dynamics problem that forms an absorbing state under a continuous change of a parameter. The information at the transition point diverges as ∝ logT , and we calculate the expression for a smooth crossover to ∝ T 0 away from the transition.