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Since Gibbs Free Energy is what is used to figure out spontaneity it doesn't need to be known throughout the process. The change in Gibbs Free Energy just has to be negative to be spontaneous and that is the biggest utilization of this concept. So it is only final and the initial states that matter not the path it took
Also, Gibbs free energy isn't something that we can directly measure. It's defined by other measurements that happen to be state functions (if you take a look at the equation, it uses things like enthalpy and entropy, which are state functions). So, I suppose it just ends up being a state function.
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