Predictive information in a nonequilibrium critical model

Abstract

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 universal order parameter to study phase transitions in physical systems. It can be used, in particular, to study nonequlibrium transitions and other exotic transitions, where a simpler order parameter cannot be identifies 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 log(T), and a smooth crossover to constant away from the transition is observed.