Notes on complexity growth rate, grand potential and partition function
We examine the complexity/volume conjecture and further investigate the possible connections between complexity and partition function. The complexity/partition function relation is then utilized to study the complexity of the thermofield double state of extended SYK models for various conditions.Th...
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Published in: | General relativity and gravitation Vol. 54; no. 5 |
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Language: | English |
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01-05-2022
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Abstract | We examine the complexity/volume conjecture and further investigate the possible connections between complexity and partition function. The complexity/partition function relation is then utilized to study the complexity of the thermofield double state of extended SYK models for various conditions.The difference between the complexity/partition function relation with the complexity/action duality comes from the fact that partition function can be evaluated from more than one saddle point, so they differ at most at the non-perturbative level. We further analyze free energy and the growth rate of complexity in the neutral AdS-Vaidya black hole formed by collapsing an uncharged spherically symmetric thin shell of null fluid. The relation between the late-time complexity growth rate and black hole/SYK wormhole phase transition is also discussed. Finally, we check the Lloyd bound with our proposal. |
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AbstractList | We examine the complexity/volume conjecture and further investigate the possible connections between complexity and partition function. The complexity/partition function relation is then utilized to study the complexity of the thermofield double state of extended SYK models for various conditions.The difference between the complexity/partition function relation with the complexity/action duality comes from the fact that partition function can be evaluated from more than one saddle point, so they differ at most at the non-perturbative level. We further analyze free energy and the growth rate of complexity in the neutral AdS-Vaidya black hole formed by collapsing an uncharged spherically symmetric thin shell of null fluid. The relation between the late-time complexity growth rate and black hole/SYK wormhole phase transition is also discussed. Finally, we check the Lloyd bound with our proposal. |
ArticleNumber | 46 |
Author | Sun, Wei Ge, Xian-Hui |
Author_xml | – sequence: 1 givenname: Wei surname: Sun fullname: Sun, Wei organization: Department of Physics, College of Sciences, Shanghai University – sequence: 2 givenname: Xian-Hui surname: Ge fullname: Ge, Xian-Hui email: gexh@shu.edu.cn organization: Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University |
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Keywords | Grand potential Partition function Black holes SYK model Complexity |
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Snippet | We examine the complexity/volume conjecture and further investigate the possible connections between complexity and partition function. The... |
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SubjectTerms | Astronomy Astrophysics and Cosmology Black holes Classical and Quantum Gravitation Complexity Differential Geometry Free energy Gravity Growth rate Mathematical and Computational Physics Partitions (mathematics) Phase transitions Physics Physics and Astronomy Quantum Physics Relativity Theory Research Article Saddle points Theoretical Thin walled shells |
Title | Notes on complexity growth rate, grand potential and partition function |
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