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