 These theses concisely capture how radically different black-hole entropy is from ordinary thermodynamical entropy. The first, as is already obvious from the Second Law of black hole mechanics, underscores the fact that black-hole entropy is proportional to the surface area of the system, not to the bulk volume as for ordinary thermodynamical systems. The second articulates the fact that the underlying entities whose statistics are conjectured to give rise to the entropy are the constituents of perhaps the most fundamental structure in contemporary physics, spacetime itself, not high-level, derivative entities such as atoms, which are not fundamental in our deepest theory of matter, quantum field theory. The third emphasizes the fact that, contrary to the way that there is no “natural” coarse-graining of underlying micro-degrees of freedom in the statistical mechanics of ordinary matter, there is a unique natural one here, intimately related to the fact that the geometry of the event horizon is unique, and the Planck scale provides a measure of units of area thought by many to be physically privileged (albeit in a sense never made entirely clear). The fourth states that the Second Law of black hole thermodynamics, generalized to include contributions from both black holes and ordinary matter (as discussed in  section 5.4  below), is not a phenomenologically derived empirical generalization, as is the Second Law for ordinary matter; rather, it follows directly from the most fundamental dynamical principle, quantum evolution, in conjunction with the basic geometry of spacetimes in general relativity. (This will be discussed further in  section 6.2  below.) This is of a piece with the fact that the Second Law for black holes in the classical regime is a theorem of pure differential geometry  (section 5.1).  