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I assume there must be quite a lot, due to the second law of thermo dynamics, but is there an estimate of how much, or a way to acquire the estimate?

Alternatively, we can calculate the entropy right after the big bang, so is there a way to know the universe's enthalpy? We can use those values to calculate the free energy.

yters
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Zero (according to my personal scale, and subject to the caveat that the universe is not at equilibrium).

The Gibbs free energy $G=U-TS+PV$. For a well-defined system in equilibrium, the temperature $T$, entropy $S$, pressure $P$, and volume $V$ all have single absolute values; the internal energy $U$ has a single value, but it is not absolute; it can only be measured relative to an arbitrary reference state. So I'm free to set the Gibbs free energy of the universe equal to zero and work from there, although I may run into problems with my assumption of equilibrium.

(The enthalpy $H=U+PV$ also can only be defined relative to an arbitrary reference state, and the same is true for the Helmholtz free energy $A=U-TS$ and the chemical potential $\mu=(dG/dN)_{T,P}$, for example.)

  • Will the free energy stay at zero as time progresses, or will you need to keep updating your values? The entropy $S$ of the universe will keep increasing, which would quickly make your value negative. – yters Sep 19 '17 at 17:12