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Causal emergence refers to a specific type of [[emergence]] phenomenon in dynamical systems, where stronger [[causal effects]] emerge at the system's macroscopic scale. In particular, for a class of [[Markov dynamical systems]], after appropriate [[coarse-graining]] of the state space, the resulting macroscopic dynamics demonstrate stronger [[causal effects]] than their microscopic counterparts. This is referred to as causal emergence <ref name=":0">Hoel E P, Albantakis L, Tononi G. Quantifying causal emergence shows that macro can beat micro[J]. Proceedings of the National Academy of Sciences, 2013, 110(49): 19790-19795.</ref><ref name=":1">Hoel E P. When the map is better than the territory[J]. Entropy, 2017, 19(5): 188.</ref>. Furthermore, the theory of causal emergence uses causal effect measurements to quantify emergence phenomena in complex systems.

Causal emergence refers to a specific type of [[emergence]] phenomenon in dynamical systems, where stronger [[causal effects]] emerge at the system's macroscopic scale. In particular, for a class of [[Markov dynamical systems]], after appropriate [[coarse-graining]] of the state space, the resulting macroscopic dynamics demonstrate stronger [[causal effects]] than their microscopic counterparts. This is referred to as causal emergence <ref name=":0">Hoel E P, Albantakis L, Tononi G. Quantifying causal emergence shows that macro can beat micro[J]. Proceedings of the National Academy of Sciences, 2013, 110(49): 19790-19795.</ref><ref name=":1">Hoel E P. When the map is better than the territory[J]. Entropy, 2017, 19(5): 188.</ref>. Furthermore, the theory of causal emergence uses measures of causal effects to quantify emergence phenomena in complex systems.