The interpretation of the inner product in terms of the kinetics of conserved and non-conserved quantities and their variational formulation introduces no new physics. However, there is conceptual utility in the unified basis from which familiar kinetic equations can be derived. Furthermore since linear combinations of inner products are inner products themselves, the variational basis can be used to extend the models described here to cases where combinations order parameters, conserved and non-conserved, are coupled.
The variational principle is straightforward to apply to cases where the free energy density is not continuously differentiable (which is the case at first-order transitions and for highly anisotropic systems). Perhaps, the example of triple junction motion could have been formulated by considering the coupled PDE's for each grain boundary in their highly anisotropic limit, but it would not have been nearly so straightforward. Furthermore, the variational formulation provides theoretical tools which we used to study whether extra small segments would be added to a triple junction in the course of its motion.
Another useful feature, is that the gradient flow and its associated theoretical machinery can be used through singular microstructural events, such as when a phase disappears or a multiple grain boundary junction goes unstable. Such methods have been used to find conditions where long facets become unstable[15].
Discrete representations of the variational principles can be used to formulate a numerical method for calculating the evolution of such systems. Suo and co-workers have used variational principles in conjunction with a finite element solver to simulate the behavior of isolated microstructural evolution when several driving forces are present simultaneously[3].