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.

我们研究了复杂度/体积猜想，并进一步研究了复杂度和配分函数之间的可能联系。然后利用复杂度/分区函数关系来研究扩展SYK模型的热场双态在各种条件下的复杂度。复杂度/分区函数关系与复杂度/作用对偶的区别在于分区函数可以是从多个鞍点进行评估，因此它们最多在非微扰水平上有所不同。我们进一步分析了中性 AdS-Vaidya 黑洞的自由能和复杂性增长率，该黑洞是由不带电的球对称空流体薄壳坍塌形成的。还讨论了后期复杂度增长率与黑洞/SYK虫洞相变之间的关系。