Simulating phase transitions by means of quasi static state changes: the capabilities of the time dependent Van der Waals equation of state

TL;DR

This paper introduces a novel simulation method called simulated expansion that uses the time-dependent Van der Waals equation to model phase transitions under gradual volume changes, capturing complex behaviors near critical points.

Contribution

It develops a new simulation approach combining the Van der Waals equation with quasi-static state changes to effectively model phase transitions under arbitrary conditions.

Findings

Successfully simulates phase transitions across subcritical, critical, and supercritical regimes.

Handles passage over singularities in susceptibility coefficients.

Provides a blueprint for general simulation approaches of phase transitions.

Abstract

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.