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
Main Authors: Sun, Wei, Ge, Xian-Hui
Format: Journal Article
Language:English
Published: New York Springer US 01-05-2022
Springer Nature B.V
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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.
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
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  fullname: Sun, Wei
  organization: Department of Physics, College of Sciences, Shanghai University
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  givenname: Xian-Hui
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  fullname: Ge, Xian-Hui
  email: gexh@shu.edu.cn
  organization: Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University
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Issue 5
Keywords Grand potential
Partition function
Black holes
SYK model
Complexity
Language English
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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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