Bekenstein Bound for Approximately Local Charged States
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915093555445760 |
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| author | Hollands, Stefan Longo, Roberto |
| author_facet | Hollands, Stefan Longo, Roberto |
| contents | We generalize the energy-entropy ratio inequality in quantum field theory (QFT) established by one of us from localized states to a larger class of states. The states considered in this paper can be in a charged (non-vacuum) representation of the QFT or may be only approximately localized in the region under consideration. Our inequality is $S(Ψ|\!| Ω) \le 2πR \, ( Ψ, H_ρΨ) + \log d(ρ) + \varepsilon$, where $S$ is the relative entropy, where $R$ is a "radius" (width) characterizing the size of the region, $d(ρ)$ is the statistical (quantum) dimension of the given charged sector $ρ$ hosting the quantum state $Ψ$, $Ω$ is the vacuum state, $H_ρ$ is the Hamiltonian in the charged sector, and $\varepsilon$ is a tolerance measuring the deviation of $Ψ$ from the vacuum according to observers in the causal complement of the region. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_03849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bekenstein Bound for Approximately Local Charged States Hollands, Stefan Longo, Roberto High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Operator Algebras Quantum Physics We generalize the energy-entropy ratio inequality in quantum field theory (QFT) established by one of us from localized states to a larger class of states. The states considered in this paper can be in a charged (non-vacuum) representation of the QFT or may be only approximately localized in the region under consideration. Our inequality is $S(Ψ|\!| Ω) \le 2πR \, ( Ψ, H_ρΨ) + \log d(ρ) + \varepsilon$, where $S$ is the relative entropy, where $R$ is a "radius" (width) characterizing the size of the region, $d(ρ)$ is the statistical (quantum) dimension of the given charged sector $ρ$ hosting the quantum state $Ψ$, $Ω$ is the vacuum state, $H_ρ$ is the Hamiltonian in the charged sector, and $\varepsilon$ is a tolerance measuring the deviation of $Ψ$ from the vacuum according to observers in the causal complement of the region. |
| title | Bekenstein Bound for Approximately Local Charged States |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2501.03849 |