Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States
Abstract
We study genuine multi-entropy in Abelian U(1)k Chern-Simons theory. For key-ring link states, where only the linking numbers between one distinguished component K and the remaining q−1 components are nonzero, we derive an exact closed-form expression for the q-partite Rényi multi-entropy for general q, level k, and Rényi index n. For q=4, this shows that the genuine multi-entropy GM(4)n collapses exactly onto the tripartite information I3,n for all n, while for q=5 it is likewise completely determined, for all n, by a linear combination of tripartite and bipartite Rényi multi-entropies. We then go beyond the key-ring class and study general four-component link states with arbitrary pairwise linking numbers. A numerical scan over Chern--Simons levels 2≤ k≤24 shows that the all-n collapse found analytically for key-ring states does not survive for generic link states. Remarkably, the collapse remains exact at n=2 for every level examined. At n=3, violations occur, within the scanned range, only when 3| k, with a further dependence on the $3$-adic valuation of k. At n=4 and n=5, violations occur for every level examined, with rates that vary strongly with k. These results show that the breakdown is not controlled simply by the zero-divisor structure of composite ℤk, but instead exhibits a nontrivial joint dependence on the Rényi index and the arithmetic structure of the Chern--Simons level.
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BibTeX
@misc{chang2026genuine,
title = {{Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States}},
author = {Yen-Cheng Chang and Kaberi Goswami and Norihiro Iizuka and Akihiro Miyata},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29627},
eprint = {2608.29627},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29627},
}
RIS
TY - UNPB
TI - Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States
AU - Yen-Cheng Chang
AU - Kaberi Goswami
AU - Norihiro Iizuka
AU - Akihiro Miyata
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29627
UR - https://arxiv.org/abs/2608.29627
AB - We study genuine multi-entropy in Abelian U(1)_k Chern-Simons theory. For key-ring link states, where only the linking numbers between one distinguished component K and the remaining q−1 components are nonzero, we derive an exact closed-form expression for the q-partite Rényi multi-entropy for general q, level k, and Rényi index n. For q=4, this shows that the genuine multi-entropy GM^(4)_n collapses exactly onto the tripartite information I_3,n for all n, while for q=5 it is likewise completely determined, for all n, by a linear combination of tripartite and bipartite Rényi multi-entropies. We then go beyond the key-ring class and study general four-component link states with arbitrary pairwise linking numbers. A numerical scan over Chern--Simons levels 2≤ k≤24 shows that the all-n collapse found analytically for key-ring states does not survive for generic link states. Remarkably, the collapse remains exact at n=2 for every level examined. At n=3, violations occur, within the scanned range, only when 3| k, with a further dependence on the $3$-adic valuation of k. At n=4 and n=5, violations occur for every level examined, with rates that vary strongly with k. These results show that the breakdown is not controlled simply by the zero-divisor structure of composite ℤ_k, but instead exhibits a nontrivial joint dependence on the Rényi index and the arithmetic structure of the Chern--Simons level.
ER -