document: This work shows how our approach based on the combination of Statistical Mechanics and nonlinear PDEs theory provides us with a novel and powerful tool to tackle phase transitions. This method leads to solution of perhaps the most known test-case that exhibits a first order phase transition (semi-heuristically described) such as the van der Waals model. In particular we have obtained the first global mean field partition function (Eq. (9)), for a system of finite number of particles. The partition function is a solution to the Klein–Gordon equation, reproduces the van der Waals isotherms away from the critical region and, in the thermodynamic limit N→∞ automatically encodes the Maxwell equal areas rule. The approach hereby presented is of remarkable simplicity, has been successfully applied to spin [17–19,14,16] and macroscopic thermodynamic systems [20,15] and can be further extended to include the larger class of models admitting partition functions of the form (4) to be used to extend to the critical region general equations of state of the form (7) including a class virial expansions.