Notes on complexity growth rate, grand potential and partition function

We examine the complexity/volume conjecture and further investigate possible connections between complexity partition function. The 2.0 states that growth rate $\mathcal{\dot{C}}\sim PV$. In standard statistics, there is a fundamental relation among $PV$, grand potential $\Omega$ function $\mathcal{Z}$. By using this relation, we are able to construct an ansatz complexity/partition then utilized study of thermofield double state extended SYK models for various conditions. black hole phase transition also discussed.