Stability with respect to bilateral perturbations

We now examine the conditions for equilibrium when the perturbations are such that may be either positive or negative. For an equilibrium state P we have (c/. 15.11) 

In particular, for perturbations at constant x and y, this condition becomes 

The relation between these conditions and the thermodynamic potentials is easily seen. Thus if we choose T andp as physical variables, then 

These conditions express the fact that if P is stable at constant T and is a minimum at this point. 

Thus stability at constant T, V corresponds to a minimum in F that at constant S, F to a minimum in U and at constant S, p 8i minimum in H. 

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