A variational approach to relaxation in rugged free energy landscapes

We develop a variational principle governing the relaxation behavior of hierarchical systems. Limiting ourselves to a particular class of models amenable of a variational treatment, we study the relaxation of rugged systems whose conformation space topology deviates from ultrametricity under selective controllable conditions. While the Debye law is obtained in the ultrametric limit, Kohlrausch relaxation is shown to be directly related to the level of ruggedness beyond the ultrametric limit.