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It is said that all thermodynamics potentials are equivalent. Some are more useful than others to describe some systems, based on which state variables are kept constant and which are allowed to vary. All thermodynamics potentials are related through a Legendre transformation. I do not know whether it is a linear transformation.

I would tend to think (based purely on intuition), that if a thermodynamics potential is minimized (for instance when the system under study reached equilibrium), then all the other thermodynamics potentials are also minimized. Is this true? Is there any caveat or is it just that simple?

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  • $\begingroup$ What parameters are you minimizing over? $\endgroup$ Commented Mar 29, 2018 at 18:42
  • $\begingroup$ None in particular. I kept my question as general as possible. I do not have any particular system under study in mind. $\endgroup$ Commented Mar 29, 2018 at 19:23

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No, it depends on the statistical ensemble you're working on, for example the Helmoltz free energy (F=U-TS) is minimized at equilibrium when the system is at fixed temperature, volume and number of particles

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  • $\begingroup$ To complete your answer, I'd like you to show that for this particular system (fixed temperature, volume and number of particles), other thermodynamics potentials aren't minimized. $\endgroup$ Commented Apr 5, 2018 at 20:58

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