Dynamical reversibility and a new theory of causal emergence based on SVD
Abstract The theory of causal emergence (CE) with effective information (EI) posits that complex systems can exhibit CE, where macro-dynamics show stronger causal effects than micro-dynamics. A key challenge of this theory is its dependence on coarse-graining method. In this paper, we introduce a fr...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | npj Complexity |
| Online Access: | https://doi.org/10.1038/s44260-025-00028-0 |
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| author | Jiang Zhang Ruyi Tao Keng Hou Leong Mingzhe Yang Bing Yuan |
| author_facet | Jiang Zhang Ruyi Tao Keng Hou Leong Mingzhe Yang Bing Yuan |
| author_sort | Jiang Zhang |
| collection | DOAJ |
| description | Abstract The theory of causal emergence (CE) with effective information (EI) posits that complex systems can exhibit CE, where macro-dynamics show stronger causal effects than micro-dynamics. A key challenge of this theory is its dependence on coarse-graining method. In this paper, we introduce a fresh concept of approximate dynamical reversibility derived from the singular value decomposition(SVD) of the Markov chain and establish a novel framework for CE based on this. We find that the essence of CE lies in the presence of redundancy, represented by irreversible and correlated information pathways within the Markov dynamics. Therefore, CE can be quantified as the potential maximal efficiency increase for dynamical reversibility or information transmission. We also demonstrate a strong correlation between the approximate dynamical reversibility and EI, establishing an equivalence between the SVD and EI maximization frameworks for quantifying CE, supported by theoretical insights and numerical examples from Boolean networks, cellular automata, and complex networks. Importantly, our SVD-based CE framework is independent of specific coarse-graining techniques and effectively captures the fundamental characteristics of the dynamics. |
| format | Article |
| id | doaj-art-732ce54bc4d54d08b71561c4553f69b7 |
| institution | OA Journals |
| issn | 2731-8753 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Complexity |
| spelling | doaj-art-732ce54bc4d54d08b71561c4553f69b72025-08-20T01:59:57ZengNature Portfolionpj Complexity2731-87532025-01-012111110.1038/s44260-025-00028-0Dynamical reversibility and a new theory of causal emergence based on SVDJiang Zhang0Ruyi Tao1Keng Hou Leong2Mingzhe Yang3Bing Yuan4School of Systems Science, Beijing Normal UniversitySchool of Systems Science, Beijing Normal UniversitySwarma ResearchSchool of Systems Science, Beijing Normal UniversitySwarma ResearchAbstract The theory of causal emergence (CE) with effective information (EI) posits that complex systems can exhibit CE, where macro-dynamics show stronger causal effects than micro-dynamics. A key challenge of this theory is its dependence on coarse-graining method. In this paper, we introduce a fresh concept of approximate dynamical reversibility derived from the singular value decomposition(SVD) of the Markov chain and establish a novel framework for CE based on this. We find that the essence of CE lies in the presence of redundancy, represented by irreversible and correlated information pathways within the Markov dynamics. Therefore, CE can be quantified as the potential maximal efficiency increase for dynamical reversibility or information transmission. We also demonstrate a strong correlation between the approximate dynamical reversibility and EI, establishing an equivalence between the SVD and EI maximization frameworks for quantifying CE, supported by theoretical insights and numerical examples from Boolean networks, cellular automata, and complex networks. Importantly, our SVD-based CE framework is independent of specific coarse-graining techniques and effectively captures the fundamental characteristics of the dynamics.https://doi.org/10.1038/s44260-025-00028-0 |
| spellingShingle | Jiang Zhang Ruyi Tao Keng Hou Leong Mingzhe Yang Bing Yuan Dynamical reversibility and a new theory of causal emergence based on SVD npj Complexity |
| title | Dynamical reversibility and a new theory of causal emergence based on SVD |
| title_full | Dynamical reversibility and a new theory of causal emergence based on SVD |
| title_fullStr | Dynamical reversibility and a new theory of causal emergence based on SVD |
| title_full_unstemmed | Dynamical reversibility and a new theory of causal emergence based on SVD |
| title_short | Dynamical reversibility and a new theory of causal emergence based on SVD |
| title_sort | dynamical reversibility and a new theory of causal emergence based on svd |
| url | https://doi.org/10.1038/s44260-025-00028-0 |
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