A Glance on the Constraint Equations

If we would confine ourself that the total system consists of these two subsystems, then no other exchange reactions would be possible. In equilibrium, we would have the total energy, the total entropy, the total volume, and the total mol number to be constant, i.e.. 

If we add the left up system to the latter system, then we have in addition an exchange of entropy from the thermal reservoir to the liquid-gas system, and we have 

We proceed now to the last step and connect the system also with a manostat by including the right up subsystem in the total system. Then the relations among the extensive variables will become 

The same what was stated for the dashed arrow for entropy flow would be valid for an additional value exchange from the manal reservoir to the liquid phase. 

In order to get the relations of the intensive variables, we have to seek for a stationary value of AUtot under the respective constraint equations that are written below the energy equation. 

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