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Difference equations of average entropies — arXiv:2608.27829

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.27829
License (as archived): CC0-1.0
Archived: 2026-10-17T11:27:20.495Z
SHA-256 of the archived text: 46b0a4ec19c39ce1ddbc03db3ccf667558bca330e89e68ecfd8baf5b9c5dcf3a
Stable URL of this page: https://metraipolis.com/documento/dc_bc5f2e92eeee

How to cite

Difference equations of average entropies — arXiv:2608.27829 — arXiv (en), https://arxiv.org/abs/2608.27829 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bc5f2e92eeee (Metraipolis archive dc_bc5f2e92eeee, sha256 46b0a4ec19c39ce1ddbc03db3ccf667558bca330e89e68ecfd8baf5b9c5dcf3a)

BibTeX

@misc{dcbc5f2e92eeee,
  title = {Difference equations of average entropies — arXiv:2608.27829},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.27829},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bc5f2e92eeee; sha256 46b0a4ec19c39ce1ddbc03db3ccf667558bca330e89e68ecfd8baf5b9c5dcf3a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.27829. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this work, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-31 in math.IT).
Categorie arXiv: Mathematical Physics (math-ph) ; Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2608.27829 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T11:07:15.588Z dalla pagina https://arxiv.org/catchup/math.IT/2026-08-31?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).