nucleation

LIT-1136: Causal Emergence 2.0: Quantifying emergent complexity

1 min read

Properties6
StatusActive — read 2026-10-29 (NOTE-1387) in full, from arXiv's own copy (v3); worth reading as the paper that recasts Hoel's causal emergence as gains in causal primitives (determinism minus degeneracy, the effectiveness, which is EI without its size term) credited to each scale along a micro→macro path of consistent coarse-grainings, with the entropy of those gains as "emergent complexity". Read it knowing that it is shown on three hand-built 8-state chains with no TPM printed, that the multi-path version is left open (LIT-1123 takes it up), that its claim to capture all macroscale causation rests on one manipulated family, and that its degeneracy formula is misprinted as 1 − H(E|C)/log₂ n.
Version2
Tagscomplex-systems, causality
ExtendsLIT-1038 — Quantifying causal emergence shows that macro can beat micro
Extended byLIT-1123 — Engineering Emergence
Cited as “paper” byNOTE-1387 — Hoel — Causal emergence 2.0

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Hoel, E. (2025). arXiv preprint.

Read in full on 2026-10-29 (NOTE-1387).

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. The framework Jansma and Hoel’s “Engineering Emergence” builds on. For QUESTION-115.

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