Using this blog as an online set of research notes (about that which I don't mind sharing ) -- suppose that we try using an equilibrium-based approach of some sort for modeling what we all know is a very non-equilibrium world. Which formulation, Helmholtz or Gibbs, works best for us?
Helmholtz free energy is at constant temperature and volume. It is denoted as A, where the defining equation is A = U-TS, where U is enthalpy, T is temperature, and S is entropy.
Gibbs free energy is at constant pressure and temperature.
The systems that we consider would be at constant volume. (E.g., constant volume of a nation, etc.) We do foresee "adding to" the system, content; e.g., adding people, adding tons of grain produced per year, adding money produced by a national treasury. These will increase the pressure, not the volume. For example, during inflation, when more money is actually being produced (or with the recent government bailout, where money is being "produced" out of thin air), we add to the "density" of money in the system; same volume, more units (money), thus greater density of dollars -- and also greater "pressure." So we will be using the Helmholtz formulation.
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