  For the study of complex synthetic and biological molecular systems by
computer simulations one is still restricted to simple model systems or to by
far too small time scales. To overcome this problem multiscale techniques are
being developed for many applications. However in almost all cases, the regions
of different resolution are fixed and not in a true equilibrium with each
other. We here give the theoretical framework for an efficient and flexible
coupling of the different regimes. The approach leads to an analog of a
geometry induced phase transition and a counterpart of the equipartition
theorem for fractional degrees of freedom. This provides a rather general
formal basis for advanced computer simulation methods applying different levels
of resolution.

Statistical Mechanics