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. 2024 Aug 12;12(1):nwae279. doi: 10.1093/nsr/nwae279

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© The Author(s) 2024. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Figure 1. — (a) An illustration of the fundamental concept of causal emergence (CE) in [19]. The effective information (EI) is denoted as in this paper. (b) A case demonstrating CE in a discrete Markov chain. The micro-dynamics consists of eight micro-states. During the coarse-graining process, the first seven states are grouped together as one macro-state, while the eighth micro-state corresponds to the second macro-state. As a result, a transition probability matrix is formed at the macro-scale, where the effective information (calculated using Equation S1), which is greater than . This difference, , indicates the occurrence of CE, as .

Inline graphic — (a) An illustration of the fundamental concept of causal emergence (CE) in [19]. The effective information (EI) is denoted as in this paper. (b) A case demonstrating CE in a discrete Markov chain. The micro-dynamics consists of eight micro-states. During the coarse-graining process, the first seven states are grouped together as one macro-state, while the eighth micro-state corresponds to the second macro-state. As a result, a transition probability matrix is formed at the macro-scale, where the effective information (calculated using Equation S1), which is greater than . This difference, , indicates the occurrence of CE, as .