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When I was studying thermodynamics potentials for the first time, I learned that keeping the pressure and the temperature constant, the Gibbs Free Energy is a minimum, also, if we maintain the temperature and the volume of a given system constant, the Helmholtz energy will be a minimum. However, when I was studying Landau theory, I was confused if one should minimize the gibbs free energy or the helmholtz free energy. For example, in the Ising Model, one expands the Free Energy and the applies landau theory. However, we need to expand the Gibbs Free Energy in the liquid-gas transition.

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marked as duplicate by heather, peterh says reinstate Monica, CuriousOne, honeste_vivere, AccidentalFourierTransform Aug 9 '16 at 14:02

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I'd say it all comes down to your physical setup.

When studying the Ising model one is usually interested in its behaviour at certain values of temperature and volume.

On the other hand, the liquid-gas transition is usually described in a pressure-temperature diagram, i.e., at different but fixed pressures and temperatures.

Bottom line: the choice of free energy depends on what physical variables describe the state your system is in.

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