Holographic principle for ordinary matter: what is the exponent?

It has been theoretically accepted for a few decades that the entropy of a black hole is equal to a quarter of its surface area (in suitable units). And since around that time ideas have been developed about an entropy limit, similarly depending on the surface area, for any physical system. This research has developed into precise statements about a 'holographic principle,' which can crudely be summarized as follows. It claims that there is a bound on the maximal amount of entropy that a physical system can have, and so on the maximal number of degrees of freedom, in a given region of space; and it claims that this bound is determined from the surface of the region. In the most basic model, this limit of the entropy is obtained directly from the surface area. Note that the actual entropy is still calculated as an extensive quantity (depending on the volume), but there would be a limit on the maximal possible amount, dependent on the surface. If this is indeed found to be a physical law, it would be one with far reaching consequences. In this talk I will present work on determining the exponent in the claimed dependency of entropy on the area, in a very basic model. Most of the talk will be concerned with clearly presenting the basic notions and ideas, and the context of my work. In other words, it assumes that the audience has had no previous exposure to this subject.