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Rosas et al. (2020)<ref name=":5" /> proposed a method using [[information decomposition]] to define and quantify causal emergence from an [[information theory|information theory]] perspective, through [[synergistic information]] or [[redundant information]]. [[Information decomposition]] is a new method to analyze the complex interrelationships of various variables in [[complex systems]]. Information decomposition represents each piece of partial information as an [[information atom]]. Partial information is projected onto a information atom using an [[information lattice diagram]]. Both synergistic information and redundant information can be represented by corresponding information atoms. This method is based on the [[non-negative decomposition theory of multivariate information]] proposed by Williams and Beer <ref name=":16">Williams P L, Beer R D. Nonnegative decomposition of multivariate information[J]. arXiv preprint arXiv:10042515, 2010.</ref>. The paper uses [[partial information decomposition]] (PID) to break down the mutual information between microstates and macrostates. However, the PID framework can only decompose the mutual information between multiple source variables and one target variable. Rosas extended this framework and proposed the integrated information decomposition method <math>\Phi ID</math> <ref name=":18">P. A. Mediano, F. Rosas, R. L. Carhart-Harris, A. K. Seth, A. B. Barrett, Beyond integrated information: A taxonomy of information dynamics phenomena, arXiv preprint arXiv:1909.02297 (2019).</ref>.
Rosas et al. (2020)<ref name=":5" /> proposed a method using [[information decomposition]] to define and quantify causal emergence from an [[information theory|information theory]] perspective, through [[synergistic information]] or [[redundant information]]. [[Information decomposition]] is a new method to analyze the complex interrelationships of various variables in [[complex systems]]. Information decomposition represents each piece of partial information as an [[information atom]]. Partial information is projected onto a information atom using an [[information lattice diagram]]. Both synergistic information and redundant information can be represented by corresponding information atoms. This method is based on the [[non-negative decomposition theory of multivariate information]] proposed by Williams and Beer <ref name=":16">Williams P L, Beer R D. Nonnegative decomposition of multivariate information[J]. arXiv preprint arXiv:10042515, 2010.</ref>. The paper uses [[partial information decomposition]] (PID) to break down the mutual information between microstates and macrostates. However, the PID framework can only decompose the mutual information between multiple source variables and one target variable. Rosas extended this framework and proposed the integrated information decomposition method <math>\Phi ID</math> <ref name=":18">P. A. Mediano, F. Rosas, R. L. Carhart-Harris, A. K. Seth, A. B. Barrett, Beyond integrated information: A taxonomy of information dynamics phenomena, arXiv preprint arXiv:1909.02297 (2019).</ref>.
=== Recent Work ===
=== Recent work ===
Barnett et al. <ref name=":6">Barnett L, Seth AK. Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems. Physical Review E. 2023 Jul;108(1):014304.</ref> proposed the concept of [[dynamical decoupling]], defining emergences based on the decoupling of macroscopic and microscopic dynamics using [[transfer entropy]]. That is, emergence is characterized by the independence of macroscopic and microscopic variables, with no causal relationship, which can be seen as a causal emergence phenomenon.
Barnett et al. <ref name=":6">Barnett L, Seth AK. Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems. Physical Review E. 2023 Jul;108(1):014304.</ref> proposed the concept of [[dynamical decoupling]], defining emergences based on the decoupling of macroscopic and microscopic dynamics using [[transfer entropy]]. That is, emergence is characterized by the independence of macroscopic and microscopic variables, with no causal relationship, which can be seen as a causal emergence phenomenon.