Beyond islands: a free probabilistic approach
Abstract We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control. We observe that the repli...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2023)040 |
| _version_ | 1827370624840892416 |
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| author | Jinzhao Wang |
| author_facet | Jinzhao Wang |
| author_sort | Jinzhao Wang |
| collection | DOAJ |
| description | Abstract We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control. We observe that the replica trick gravitational path integral is combinatorially matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector respectively. The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply. It also helps to justify this gravitational replica trick as a soluble Hausdorff moment problem. We then work out how the free convolution formula can be evaluated using free harmonic analysis, which also gives a new free probabilistic treatment of resolving the separable sample covariance matrix spectrum. The free convolution formula suggests that the quantum information encoded in competing quantum extremal surfaces can be modelled as free random variables in a finite von Neumann algebra. Using the close tie between free probability and random matrix theory, we show that the PSSY model can be described as a random matrix model that is essentially a generalization of Page’s model. It is then manifest that the island formula is only applicable when the convolution factorizes in regimes characterized by the one-shot entropies. We further show that the convolution formula can be reorganized to a generalized entropy formula in terms of the relative entropy. |
| first_indexed | 2024-03-08T10:18:16Z |
| format | Article |
| id | doaj.art-f0922f5f0003442f96f0b4fd339c0059 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T10:18:16Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f0922f5f0003442f96f0b4fd339c00592024-01-28T12:12:38ZengSpringerOpenJournal of High Energy Physics1029-84792023-10-0120231017210.1007/JHEP10(2023)040Beyond islands: a free probabilistic approachJinzhao Wang0Institute for Theoretical Physics, ETH ZürichAbstract We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control. We observe that the replica trick gravitational path integral is combinatorially matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector respectively. The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply. It also helps to justify this gravitational replica trick as a soluble Hausdorff moment problem. We then work out how the free convolution formula can be evaluated using free harmonic analysis, which also gives a new free probabilistic treatment of resolving the separable sample covariance matrix spectrum. The free convolution formula suggests that the quantum information encoded in competing quantum extremal surfaces can be modelled as free random variables in a finite von Neumann algebra. Using the close tie between free probability and random matrix theory, we show that the PSSY model can be described as a random matrix model that is essentially a generalization of Page’s model. It is then manifest that the island formula is only applicable when the convolution factorizes in regimes characterized by the one-shot entropies. We further show that the convolution formula can be reorganized to a generalized entropy formula in terms of the relative entropy.https://doi.org/10.1007/JHEP10(2023)040Black Holes2D GravityMatrix ModelsModels of Quantum Gravity |
| spellingShingle | Jinzhao Wang Beyond islands: a free probabilistic approach Journal of High Energy Physics Black Holes 2D Gravity Matrix Models Models of Quantum Gravity |
| title | Beyond islands: a free probabilistic approach |
| title_full | Beyond islands: a free probabilistic approach |
| title_fullStr | Beyond islands: a free probabilistic approach |
| title_full_unstemmed | Beyond islands: a free probabilistic approach |
| title_short | Beyond islands: a free probabilistic approach |
| title_sort | beyond islands a free probabilistic approach |
| topic | Black Holes 2D Gravity Matrix Models Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP10(2023)040 |
| work_keys_str_mv | AT jinzhaowang beyondislandsafreeprobabilisticapproach |