  A simple kinetic model, which is presumably minimum, for the phase transition
of the van der Waals fluid is presented. In the model, intermolecular
collisions for a dense gas has not been treated faithfully. Instead, the
expected interactions as the non-ideal gas effect are confined in a
self-consistent force term. Collision term plays just a role of thermal bath.
Accordingly, it conserves neither momentum nor energy, even globally. It is
demonstrated that (i) by a natural separation of the mean-field self-consistent
potential, the potential for the non-ideal gas effect is determined from the
equation of state for the van der Waals fluid, with the aid of the balance
equation of momentum, (ii) a functional which monotonically decreases in time
is identified by the H theorem and is found to have a close relation to the
Helmholtz free energy in thermodynamics, and (iii) the Cahn--Hilliard type
equation is obtained in the continuum limit of the present kinetic model.
Numerical simulations based on the Cahn--Hilliard type equation are also
performed.
