Criteria for thermodynamical equilibrium

Now we consider the criteria which can used to judge whether a system is in its equilibrium state under given conditions. We already know that for a closed system, as it changes from a non-equilibrium state to the equilibrium state, the entropy increases. 

It can be stated in a different way that for a closed system the entropy is maximized in the equilibrium state. 

In considering the equilibrium state of a system at constant temperature and volume, we construct a closed system which consists of the system (subsystem 1) under consideration and a thermal reservoir (subsystem 2) with the temperamre T. When the two systems are brought into thermal contact, energy is exchanged between subsystem 1 and subsystem 2. Because the 

At constant temperature and volume, the equilibrium state has the minimum Helmholtz free energy. 

At constant temperature and pressure, the equilibrimn state has the minimum Gibbs free 

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ANALYTICAL CRITERIA FOR THERMODYNAMIC EQUILIBRIUM derivative equations... 

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