  The decomposition kinetics of a solid-solution into separate phases are
analyzed with an equation of motion initially developed to account for
dissipative processes in quantum systems. This equation and the
steepest-entropy-ascent quantum thermodynamic framework of which it is a part
make it possible to track kinetic processes in systems in non-equilibrium,
while retaining the framework of classical equilibrium thermodynamics. The
general equation of motion is particularized for the case of the decomposition
of a binary alloy, and a solution model is used to build an approximate energy
eigenstructure, or pseudo-eigenstructure, for the alloy system. This equation
is then solved with the pseudo-eigenstructure to obtain a unique reaction path
and the decomposition kinetics of the alloy. For a hypothetical solid-solution
with a miscibility gap at low temperatures, the conditions under which this
framework predicts a continuous transformation path (spinodal decomposition) or
a discontinuous one (nucleation and growth) are demonstrated.
