Choosing the correct free energy functional is critical when developing thermodynamically consistent phase field models. We show that the grand-potential phase field model minimizes the Helmholtz free energy when mass conservation is imposed. While both functionals are at a minimum at equilibrium, the Helmholtz free energy decreases monotonically with time in the grand-potential phase field model, whereas the grand potential does not. Minimizing the grand potential implies a different problem where a system can exchange mass with its surroundings at every point, leading to a condition of isochemical potential and invalidating mass conservation of the system.

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• Entropy production
• Interface & surface thermodynamics
• Irreversible processes
• Nonequilibrium & irreversible thermodynamics
• Alloys
• Materials modeling
• Phase-field modeling