Kinetics of Disorder →Order Transformations: Thermodynamic Theory Versus Kinetic Rate Theory

In alloys near thermodynamic equilibrium, the state variables change slowly enough so that the alloy is able to sample all microstates available to it. The entropy is well-defined. It is not surprising, although not strictly necessary, for the kinetics to follow the steepest gradient of the free energy function. Far from thermodynamic equilibrium, however, we expect the free energy function to be less useful. An internal energy can be defined, of course, and an entropy can be defined, for example, by counting the microstates accessible to a corresponding system having the same state variables, but in equilibrium at a different temperature. During the kinetic evolution of the alloy, however, not all of these microstates are encountered with equal probability. No physical mechanism of atom movement allows for direct transitions between arbitrary pairs of microstates. If many elementary kinetic events are required for the system to pass from one specific state to another, the internal energy may have already begun to relax before the microstates of the second state are adequately sampled