Dynamical Reversibility and A New Theory of Causal Emergence

The theory of causal emergence based on effective information suggests that complex systems may exhibit a phenomenon called causal emergence, where the macro-dynamics demonstrate a stronger causal effect than the micro-dynamics. However, a challenge in this theory is the dependence on the method used to coarse-grain the system. In this letter, we propose a novel notion of dynamical reversibility and build a coarse-graining method independent theory of causal emergence based on that. We not only found an approximately asymptotic logarithmic relation between dynamical reversibility and effective information for measuring causal effect, but also propose a new definition and quantification of causal emergence that captures the intrinsic properties of the Markov dynamics. Additionally, we also introduce a simpler method for coarse-graining large Markov chains based on the dynamical reversibility.