bounding surface. The same holds then for the number of available DoF in $V$. This is the spacelike holographic principle.

In a series of papers Brustein et al. developed a point of view that relates typical fluctuation results of quantum mechanical observables in quantum field theory with the area-law-like behavior of entanglement entropy and BH-entropy (cf. e.g. [@Bru]). We already made a brief remark to this approach in [@Requ1]. We note that we arrived at related results using different methods in another context (see e.g. [@CMP50] and [@JMP43]). As a more detailed comment would lead us too far astray, we plan to discuss this subject matter elsewhere.

What we are going to show in the following is that the mechanism leading to the strange area-behavior of the entropy of an enclosed volume, $V$, is considerably subtler as usually envisaged. On the one hand, we will show that the number of elementary DoF contained in $V$ is in principle proportional to the volume. On the other hand we infer from observations on the macroscopic or mesoscopic scale that the fluctuations of e.g. the energy are strongly anticorrelated. However, as long as this compensation mechanism is short-ranged, we would still have a 