Difference between thermodynamic potentials and free energy Reading this post, How can one say that if we subtract "TS" from "U" then what we get is free energy? I read that:

Strictly speaking, free energy is the difference in the value of the
  potential in the non-equilibrium state and the equilibrium state.
  Therefore, free energy is a function of two states: the initial
  non-equlibrium state and final equilibrium state. Often this subtle
  detail is ignored and one tends to call the Gibbs function as the
  Gibbs free energy and so on. Well this is wrong but happens very
  often.

I'm curious about this detail, which I cannot find elsewhere. To me, free energy was directly F or G. Is he right? why don't you say free energy then to U or H? Is it between a non-equilibrium state and an equilibrium state or between 2 equilibrium states?
I would comment that answer, but the user has been inactive for 5 years...
 A: I think it is because of different usage of terminology. The author calls the state function "Gibbs potential" and the difference between two states (nonequilibrium or equilibrium, their nature is of no relevance) as "Gibbs free energy". However I would personally call the former "absolute Gibbs free energy" (typically intractable and not very relevant) and the latter "Gibbs free energy difference" (which is what most people care about). People often colloquially shorten the latter to just "Gibbs free energy", hence the confusion.
A: The statement that

free energy is a function of two states: the initial non-equilibrium state and final equilibrium state

is an imprecise and confusing way to explain things. What this means is that the amount of useful work that can be extracted when a system goes to equilibrium is the difference in the thermodynamic potential, Gibbs (if $P$, $T$ and $N$ are constant) or Helmholtz (if $V$, $T$ and $N$ are constant):
$$
   W_\text{max} = 
   \begin{cases}
        \Delta A_{12} & (T,V,N) = \text{const}\\
        \Delta G_{12} & (T,P,N) = \text{const}
   \end{cases}
$$
The term "free energy" is older and the preferred term is Gibbs energy ($G=U-TS$) and Helmholtz energy ($A = U-TS$), both of which are functions of the state. The poster of the quote you mention uses 'free energy' to mean 'useful work', but most people will take 'free energy' to refer to either $A$ or $G$.
