更改

==Causal Emergence==

==Causal Emergence==

With the metric of Effective Information (EI) in place, we can now discuss causal emergence in Markov chains. For a Markov chain, an observer can adopt a multi-scale perspective to distinguish between micro and macro levels. First, the original Markov transition matrix P defines the micro-level dynamics. Second, after a coarse-graining process that maps microstates into macrostates (typically by grouping microstates together), the observer can obtain a macro-level transition matrix P′, which describes the transition probabilities between macrostates. We can compute EI for both dynamics. If the macro-level EI is greater than the micro-level EI, we say that the system exhibits causal emergence.

With the metric of Effective Information (EI) in place, we can now discuss causal emergence in Markov chains. For a Markov chain, an observer can adopt a multi-scale perspective to distinguish between micro and macro levels. First, the original Markov transition matrix P defines the micro-level dynamics. Second, after a [[coarse-graining for Markov chain]] that maps microstates into macrostates (typically by grouping microstates together), the observer can obtain a macro-level transition matrix P′, which describes the transition probabilities between macrostates. We can compute EI for both dynamics. If the macro-level EI is greater than the micro-level EI, we say that the system exhibits causal emergence.

[[文件:CE.png|替代=因果涌现示意图|500x500像素|链接=https://wiki.swarma.org/index.php/%E6%96%87%E4%BB%B6:CE.png]]

[[文件:CE.png|替代=因果涌现示意图|500x500像素|链接=https://wiki.swarma.org/index.php/%E6%96%87%E4%BB%B6:CE.png]]