Theory of the isoconfigurational ensemble

In molecular dynamics, we can reveal properties of molecular systems (with a finite number of molecules) to macroscopic systems by appropriate ensemble averaging via known statistical mechanical relationships. The isoconfigurational ensemble has revealed clear signatures of dynamical heterogeneities in glassy systems and supercooled liquids (see my publications). However, there are questions pertaining to its connection to fundamental statistical mechanics. Is there a clearly defined theory that can address the following questions:

1) are averaging the particles appropriate and at what time scales?

2) what is the physical meaning behind heterogeneities revealed?

3) what is the formal connection to ensembles as defined in statistical mechanics?

4) can this technique be extended to other systems? what do the results mean?