Hierarchically constrained dynamics of the configurational coordinate for rate processes in complex systems

A class of models has been proposed for the dynamics of the local configurational changes governing rate processes in complex systems. Models that fall into this class are based on a hierarchical picture of a complex object. In addition, they include constraints in order to take into account the coupling between local and global configurational rearrangements of a complex object. Using the simplest formulation possible, we have shown that the net effect of global modes on the dynamics of the configuration coordinate is the anomalous time-dependent diffusivity. The latter arises only below a certain temperature prescribed by the energy distribution of configurational substates.