  The van der Waals-Maxwell phase transition theory is among the oldest and the
most simplest theories describing thermodynamic phase transitions in physics.
Studying the complex Sachdev-Ye-Kitaev (cSYK) model numerically and deriving a
new black hole solution in Jackiw-Telteiboim (JT)gravity analytically, we
investigate how these models behave like the van der Waals-Maxwell liquid-gas
model. The cSYK model exhibits first order phase transition terminating at the
critical point, while the charged black hole in JT gravity shows a clear van
der Waals-Maxwell like phase structure. In the absence of charge, the
corresponding neutral black hole still has the Hawking-Page phase transition.
The black hole solution also provides the first example in JT gravity yielding
the van der Waals-Maxwell like phase structure.
