It’s a little bit of black magic that plays a crucial role in the way we think about entropy. In Figure 45 we’ve portrayed how coarse-graining works; it simply divides up the space of all states of a system into regions (macrostates) that are indistinguishable by macroscopic observations. Every point within one of those regions corresponds to a different microstate, and the entropy associated with a given microstate is proportional to the logarithm of the area (or really volume, as it’s a very high-dimensional space) of the macrostate to which it belongs.
