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!Method!!Consider Causality?!!Involve Coarse-graining?!!Applicable Dynamical Systems!!Measurement Index

!Method!!Consider Causality?!!Involve Coarse-graining?!!Applicable Dynamical Systems!!Measurement Index

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|Hoel's causal emergence theory||Dynamic causality, the definition of EI introduces do-intervention||Requires specifying a coarse-graining method||Discrete Markov dynamics||Dynamic causality: effective information

|Hoel's causal emergence theory [1]||Dynamic causality, the definition of EI introduces do-intervention||Requires specifying a coarse-graining method||Discrete Markov dynamics||Dynamic causality: effective information

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|Rosas's causal emergence theory||Approximation by correlation characterized by mutual information||When judged based on synergistic information, no coarse-graining is involved. When calculated based on redundant information, a coarse-graining method needs to be specified.||Arbitrary dynamics||Information decomposition: synergistic information or redundant information

|Rosas's causal emergence theory [37]||Approximation by correlation characterized by mutual information||When judged based on synergistic information, no coarse-graining is involved. When calculated based on redundant information, a coarse-graining method needs to be specified.||Arbitrary dynamics||Information decomposition: synergistic information or redundant information

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|Causal emergence theory based on reversibility||Dynamic causality, EI is equivalent to approximate dynamical reversibility||Does not depend on a specific coarse-graining strategy||Discrete Markov dynamics||Approximate dynamical reversibility: <math>\Gamma_{\alpha}</math>

|Causal emergence theory based on reversibility[26]||Dynamic causality, EI is equivalent to approximate dynamical reversibility||Does not depend on a specific coarse-graining strategy||Discrete Markov dynamics||Approximate dynamical reversibility: <math>\Gamma_{\alpha}</math>

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|Dynamic independence||Granger causality||Requires specifying a coarse-graining method||Arbitrary dynamics||Dynamic independence: transfer entropy

|Dynamic independence[40]||Granger causality||Requires specifying a coarse-graining method||Arbitrary dynamics||Dynamic independence: transfer entropy

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