About the time dependency of the Van der Waals equation of state : About the time dependency of the Van der Waals equation of state

The Van der Waals equation is one of the prototypes of the equation of states for realistic systems because of the first time introduction of excluded volume and particle interactions into theoretical considerations. On the other side the simulated annealing (and the similar simulated compressing) approach applies the time dependency to one of the variables of state performing simulations as quasi static state changes. The combination of this time dependency and the VdW-EoS enables a generalization of such considerations up to the simulations of time dependent processes like phase transitions and the obtaining of phase transition kinetics. Simple mathematical deductions starting with the time dependent Van der Waals equation allow not only the direct derivation of the simulated annealing/compressing method (isochor condition) but also the derivation of two so called differential simulated changes of state methods (isobar and isotherm conditions). These new methods enable the performation of phase transition simulations of hypocritical substances (e.g. crystallization/melting or condensation/evaporation) forward and backward in an hysteresis manner without the danger of crashing the simulations by achieving infinite values of the corresponding suszeptibility coefficients. The reason is quite simple: Such processes which occure very often in nature seem to run not by means of continous temperature or pressure increasing/decreasing but by means of a speed limited steady volume expansion. The demonstrated method handling the Van der Waals equation as a time dependent one may be a blue print for considering other equations of state by the same manner.