Why does the Gibbs free energy not decrease ad infinitum? I would like to ask which guarantees if the Gibbs free energy has a minimum in closed system (e.g. in a chemical reaction system) at constant pressure and temperature? Why does it not decrease ad infinitum?  
 A: As this is a closed system but not an isolated system, so we can add heat to the system. And, at the same time, we can increase its volume. By doing so, we may be able to keep temperature and pressure and increase entropy (note microstate increases because the position opportunity is increased). If this can reduce Gibbs free energy continuously? I guess there is a limit because the particle speed is capped by the light speed. At certain volume, adding heat may not be able to keep up pressure. By then, the volume can not be further increased as well. So Gibbs free energy cannot decrease forever. 
A: We must find the minimum of $G$ taking into account the constraints imposed on the system.
An evident example : for a chemical reaction, when all the products have disappeared, the system can no longer evolve. So the interval of evolution is evidently limited.
Still for a chemical reaction, if the products are in excess, we can plot the evolution of $G$ as a function of the extend of the reaction $\xi$ and find the minimum which corresponds to the law of mass action.
A: Interatomic potentials have a finite minimum which means that the overall enthalpy of the system has a finite minimum. And any finite system also has a finite maximum entropy.
