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If was wondering about the relation between

*information*and

*entropy*, in the following context.

The way I understand Gerard 't Hoofd's holographic principle is this. We know that the entropy of a black hole is A/4. Now suppose that a volume V was found to have an excess in entropy of a black hole just big enough to fit inside V. By throwing in additional matter we could form such a black hole. But... this gives problems with the second law. The entropy decreases by this proces. Conclusion: the maximum entropy of a volume V is given by the area of it's boundary (in certain units).

In an article in the Scientific American (aug. 2003) Bekenstein says that the maximum

*information*in a given volume is bounded by the area.

I don't see this relation between entropy and information clear.