Information Flow in First-Order Potts Model Phase Transition

Abstract: Phase transitions abound in nature and society, and, from species extinction to stock market collapse, their prediction is of widespread importance. In earlier work we showed that Global Transfer Entropy, a general measure of information flow, was found to peak away from the transition on the disordered side for the Ising model, a canonical second-order transition. Here we show that (a) global transfer entropy also peaks on the disordered side of the transition of finite first-order transitions, i.e., those which have finite latent heat and no correlation length divergence, such as ecology dynamics on coral reefs, and (b) analysis of information flow across state boundaries unifies both transition orders. We obtain the first information-theoretic result for the high-order Potts model and the first demonstration of early warning of a first-order transition. The unexpected earlier finding that global transfer entropy peaks on the disordered side of a transition is also found for finite first-order systems, albeit not in the thermodynamic limit. By noting that the interface length of clusters in each phase is the dominant region of information flow, we unify the information theoretic behaviour of first and second-order transitions.