I.I Stability Conditions

The conditions derived in section I.G are similar to the well known requirements for mechanical stability. A particle moving in an external potential U settles to a stable equilibrium at a minimum value of U . In addition to the vanishing of the force −U , this is a consequence of the loss of energy to frictional processes. Stable equilibrium occurs at a minimum of the potential energy. For a thermodynamic system, equilibrium occurs at the extremum of the appropriate potential, for example at the maximum value of entropy for an isolated system. The requirement that spontaneous changes should always lead to an increased entropy, places important constraints on equilibrium response functions, discussed in this section. Consider a homogeneous system at equilibrium, characterized by intensive state func­ tions (T, J, μ), and extensive variables (E, x, N). Now imagine that the system is arbitrar­ ily divided into two equal parts, and that one part spontaneously transfers some energy to the other part in the form of work or heat. The two subsystems, A and B, initially have the same values for the intensive variables, while their extensive coordinates satisfy EA + EB = E, xA + xB = x, and NA + NB = N. After the exchange of energy between the two subsystems, the coordinates of A change to