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LIT-1129: Dynamical Reversibility and A New Theory of Causal Emergence based on SVD

1 min read

Properties5
StatusActive — read 2026-10-29 (NOTE-1399) in full, from arXiv's own copy (v6, with the supplement and proofs); worth reading for Γ_α = Σσᵢ^α as a measure of how near a transition matrix is to a permutation, the bounds log Γ_α − log N ≤ EI ≤ (2/α) log Γ_α, and causal emergence read off the spectrum as the gain in average singular value when values at or below ε are dropped. Read it knowing that with ε > 0 the measure depends on ε and is positive at some ε for every matrix whose singular values are not all equal, so "independent of coarse-graining" holds only for the rank test; that its Proposition 5, that its lumping commutes with the dynamics for any grouping, is false; and that the equivalence with EI maximization rests on Hoel's Boolean-network examples.
Version2
Tagscomplex-systems, causality
ExtendsLIT-1038 — Quantifying causal emergence shows that macro can beat micro
Cited as “paper” byNOTE-1399 — Zhang et al. — Dynamical reversibility and causal emergence based on SVD

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Zhang, J., Tao, R., Leong, K. H., Yang, M. & Yuan, B. (2024). arXiv preprint.

Read in full on 2026-10-29 (NOTE-1399).

Why this is here

Registered as a candidate for the follow-up in Hoel’s line that A10 of the exchange of 2026-10-16 cited (“2024/2025”), on searching for coarse-grainings rather than assuming them. That paper could not be identified uniquely (curation entries of 2026-10-16); the owner asked for every candidate to be filed. Not Hoel’s own, but the 2024 candidate that answers the description best: it addresses causal emergence’s dependence on the coarse-graining method. Its singular-value form is close to CLAIM-164’s gaps. For QUESTION-115.

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