  The Van der Waals equation (VdW-EoS) is a prototype equation of state for
realistic systems, because it contains the excluded volume and the particle
interactions. Additionally, the simulated annealing (and the similar simulated
compressing) approach applies the time dependence on to one of the variables of
state to simulate quasi static state changes. The combination of both enables
the simulation of time dependent processes like phase transitions of
subcritical, critical and supercritical substances on every arbitrary condition
including a passage over points of singularity of the corresponding
susceptibility coefficients. This is achieved by a new simulation approach
called simulated expansion. This approach makes the simulation comparable to
natural processes which exhibit gradual changes in volume, rather than changes
in temperature or pressure, as exercised in simulated annealing or compressing.
The demonstrated method here serves as a blue print for more general classes of
simulation approaches.
