If I have some arbitrary Thermodynamic system, and I want to find the equilibrium state what do I do? Lets say that I know Internal energy: U(S,V) Helmholtz free energy: F(T,V) Enthalpy: H(S,P) Gibbs free energy: G(T,P) (I omitted the dependence on particles N) I've been discussing this with some friends. They say that just minimize one of them and you have the state. You can then just transform back and forth between them to get the other state variables, meaning if I minimize U and find the S and V that minimizes the system, you can then just find T and V from them (from some equation of state), and they are the values of T and V that minimizes F(T,V). I think this is wrong I understood it as, I need to take a look at my system. If I choose that my system have a fixed S and V when the system is going towards equilibrium, then I can minimize U and I find the S and V, for the system in equilibrium. But if I have minimized H for example, and found S and P they wouldn't be the correct values for my system in equilibrium (because I assumed fixed S and V, not fixed S and P), that is the two S's found wouldn't agree, and if I could determine V from the S and P found from minimizing H, that wouldn't agree with the one from minimizing U. I hope you understand what i'm asking. You have to minimize the correct potential depending one the situation you are describing, not just some random one. I'm not meaning what would be the easiest, but that you simply can't choose any potential. by the way, when we are talking about a system at fixed S and V, and then say that U is a function of S and V, seems a bit strange, I guess that if we take some general system U is a function of those, we then determine U as a function of those, we then say that we keep S and V fixed for our system, so that we have to minimize U (assuming that I was right in my first quaestion), but saying that we keep S and V fixed doesn't change that U is a function of S and V, the only important thing is that when saying this, we say we have to minimize U. Is this right or am I completely confused?