number of nearly independently fluctuating clusters of elementary DoF which again happens to be proportional to the volume as the cluster size is roughly equal to the correlation length. So the conclusion seems to be inescapable that the patterns of vacuum fluctuations must actually be [long-range correlated]{} on a microscopic scale.

But we showed in [@Requ1] or [@R5] in quite some detail that even systems, displaying long-range correlations, will usually have an entropy which is proportional to the volume. A typical example is a (quantum) crystal ([@Requ1],[@R5]). It is certainly correct that below a phase transition point a system of particles in the crystal phase has a smaller entropy than in the liquid or gas phase, but still the entropy happens to be an extensive quantity. The reason is in our view that the system develops, as a result of the long-range correlations, new types of collective excitations (e.g. lattice phonons) which serve as new collective DoF. Approximately they may be treated as a gas of weakly interacting elementary modes with the usual extensive entropic behavior.

That is, the holographic principle entails that the elementary DoF have to be long-range anticorrelated (cf. also the remarks in [@H4] or sect.7 of 