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Proof of the entropic $c$-theorem — arXiv:2610.40874

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40874
License (as archived): CC0-1.0
Archived: 2026-11-02T05:09:25.761Z
SHA-256 of the archived text: b5c749ff6d93c3f6135be9a3cd6a5959df326933eb2ff86d833a17b09c5a1cab
Stable URL of this page: https://metraipolis.com/documento/dc_aab2bc05bebb

How to cite

Proof of the entropic $c$-theorem — arXiv:2610.40874 — arXiv (en), https://arxiv.org/abs/2610.40874 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_aab2bc05bebb (Metraipolis archive dc_aab2bc05bebb, sha256 b5c749ff6d93c3f6135be9a3cd6a5959df326933eb2ff86d833a17b09c5a1cab)

BibTeX

@misc{dcaab2bc05bebb,
  title = {Proof of the entropic $c$-theorem — arXiv:2610.40874},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40874},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_aab2bc05bebb; sha256 b5c749ff6d93c3f6135be9a3cd6a5959df326933eb2ff86d833a17b09c5a1cab},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40874. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove an entropic $c$-theorem in two dimensions by constructing a $c$-function from the mutual information between spacelike separated wedges, defined through the relative entropy. The proof follows Casini and Huerta's, with strong subadditivity of entanglement entropy replaced by increasing differences of the mutual information, which we prove directly in the continuum from the split property and standard properties of relative entropy. The benefit of relative entropy is that every quantity we use is finite and no cutoff ever needs to be introduced. The assumptions of the theorem are only the standard axioms of algebraic quantum field theory, the split property with finite mutual information across a gap (both implied by modular $p$-nuclearity), and a finite ultraviolet bound on the resulting $c$-functions. We also note that, formally, the $c$-function is proportional to the minimal averaged null energy of a state that reproduces the vacuum correlations between the two wedges.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: High Energy Physics - Theory (hep-th) ; Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.40874 — 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 2026-11-02T04:52:13.364Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).