Thermodynamics, 5th Edition

(1.10.2d)

The energy of the system thus spontaneously diminishes, in agreement with earlier statements.

Case (c). In this particular application, by external intervention, one removes the system slightly from its quiescent state where dS=dV=dn_i=0 (all i). The intervention is then terminated while still retaining the constraints. If, as a response, the system returns to its initial state, then δE=0; i.e., the energy of the system has reached an extremum, because of Eq. (1.10.2d), a minimum, consistent with the original constraints. Otherwise uncontrolled processes take place until a new quiescent state is reached. This is yet another statement ...