The energy inequality expression

Stable equilibrium states are the target destination for aU metastable states, once their constraints are released. What equations refer to this process We try here to make these important relationships fairly intuitive. 

Equation (4.8) can also be written in the form of a total differential as 

The USV surface defined by this equation has an energy U defined for given values of the two constraint variables S and V. It refers to changes in energy between stable equilibrium states of a system (which may take place reversibly or irreversibly). At given values of S and V, a metastable state will have greater values of U than those represented by this surface, and it will be held in that state by a third constraint of some kind. Examples of equations having a third constraint are shown in 4.7. 

Consider the wire-stretching example (Equation 4.12) again. If we impose a third constraint, i.e., we do non-PV work on the system like stretching the wire, we increase the value of U dl and therefore f dl is positive). When the constraint is released, the wire shrinks back to its former length, and the system lowers its U irreversibly to the stable value. During this process, the shrinking 

That s like supposing a ball can roll downhill reversibly. 

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