(In the following discussion, when I use the word "always", I mean "as good as always" if you're willing to ignore exotic systems with negative temperature and such)(adsbygoogle = window.adsbygoogle || []).push({});

In the following discussion I will assume we're working in a heat bath withconstant T and P:

So there are several ways to see the total Gibbs free energy of an object, defined G = U - TS + PV, is negative.

Two simple ways:

(*) Chemical potential is defined as [tex]\mu = -T \left( \frac{dS}{dN} \right)_{U,V}[/tex] and thus is always negative. We also can prove [tex]G = \mu N[/tex].

(*) We know [tex]T \Delta S \geq Q = Q + P \Delta V - P \Delta V \geq Q + P \Delta V + W = \Delta U + P \Delta V[/tex] so [tex]TS \geq U + PV[/tex] or [tex]G \leq 0[/tex].

So now the problem is, when we 'make something' its G function goes from zero to something negative (as was just shown in two ways). This implies it should happen spontaneously, since in constant T and P the second law becomes "G goes to a minimum".

So does this say things should randomly pop into existence? Obviously there is a thinking error?

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# According to Thermodynamics Everything should Pop into Existence?

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