Thermodynamic driving forces in different systems

To complete the analogy to Helmholtz free energy in NVT systems  

NPT systems that minimize Gibbs free energy maximize Z. Therefore G is a useful thermodynamic potential for NPT systems NPT systems spontaneously move down gradients in Gibbs free energy. 

In Section 1.3.2 we saw that the Gibbs formula for entropy applies equally well to an isolated system as to a closed isothermal system. To determine whether or not this formula applies to NPT systems as well, we can substitute the NPT probability law of Equation (1.18) into Equation (1.15)  

In the previous three sections we have seen that three different thermodynamic driving forces are associated with three different systems (the NVE, NVT, and NPT systems). The driving forces for the three systems are summarized in Table 1.1. In the simplest case (the NVE system), in which the system does not exchange energy or material with its surroundings, the isolated system moves naturally to 

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