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PreprintarXiv licencearXiv

Permutation order governs basin entropy in critical one-input Boolean networks

  • Ruodan Liu
  • Ahana Ghosh
  • Sean Campbell
  • Venkata Sai Narayana Bavisetty
  • Matthew Wheeler
  • Claus Kadelka
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Abstract

Basin entropy measures uncertainty about a network's long-term behavior. For every critical one-input synchronous Boolean network with m relevant nodes, we show that the permutation structure induced by its feedback loops determines basin entropy, up to a universal error. Although the loops oscillate independently, their relative phases can be offset, producing a deviation from additivity that can grow linearly in m. Yet at the ensemble level, a previously derived additive prediction is preserved through the first subleading term, with the discrepancy appearing at order ln mlnln m.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026permutation,
  title = {{Permutation order governs basin entropy in critical one-input Boolean networks}},
  author = {Ruodan Liu and Ahana Ghosh and Sean Campbell and Venkata Sai Narayana Bavisetty and Matthew Wheeler and Claus Kadelka},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08532},
  eprint = {2611.08532},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08532},
}
RIS
TY  - UNPB
TI  - Permutation order governs basin entropy in critical one-input Boolean networks
AU  - Ruodan Liu
AU  - Ahana Ghosh
AU  - Sean Campbell
AU  - Venkata Sai Narayana Bavisetty
AU  - Matthew Wheeler
AU  - Claus Kadelka
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.08532
UR  - https://arxiv.org/abs/2611.08532
AB  - Basin entropy measures uncertainty about a network's long-term behavior. For every critical one-input synchronous Boolean network with m relevant nodes, we show that the permutation structure induced by its feedback loops determines basin entropy, up to a universal error. Although the loops oscillate independently, their relative phases can be offset, producing a deviation from additivity that can grow linearly in m. Yet at the ensemble level, a previously derived additive prediction is preserved through the first subleading term, with the discrepancy appearing at order ln mlnln m.
ER  -