PreprintCC BY 4.0arXiv
Strong subadditivity of topological entropy on the torus: Rényi order and non-Abelian structure
Abstract
We classify canonical Rényi strong subadditivity on an unpunctured torus for finite unitary modular categories. For all pure logical states and admissible region pairs, validity at 0<alpha<1 is equivalent to Abelianity; at alpha=1 it is universal. Each finite non-Abelian group G has a pure untwisted D(G) fixed-point ground state with an order-two violation under ordinary edge partial traces. A specified local-filter D(S_3) family changes reduced spectra; its fixed-cut deficit tends to the negative fixed-point value over a small size-independent interval in a controlled joint limit.
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BibTeX
@misc{liang2026strong,
title = {{Strong subadditivity of topological entropy on the torus: Rényi order and non-Abelian structure}},
author = {Yi Liang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20078},
eprint = {2610.20078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20078},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Strong subadditivity of topological entropy on the torus: Rényi order and non-Abelian structure
AU - Yi Liang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.20078
UR - https://arxiv.org/abs/2610.20078
AB - We classify canonical Rényi strong subadditivity on an unpunctured torus for finite unitary modular categories. For all pure logical states and admissible region pairs, validity at 0<alpha<1 is equivalent to Abelianity; at alpha=1 it is universal. Each finite non-Abelian group G has a pure untwisted D(G) fixed-point ground state with an order-two violation under ordinary edge partial traces. A specified local-filter D(S_3) family changes reduced spectra; its fixed-cut deficit tends to the negative fixed-point value over a small size-independent interval in a controlled joint limit.
ER -