Why does entropy invariably increase?

It's simple really. The Universe runs on BigNum rational arithmetic. As small perturbations are accumulated, ever larger rationals are required to represent state without destroying information or losing accuracy.

>>7
Possibly, but there were some experimental results that suggested smaller granularity than that. It would be nice if they were actually the smallest units since it would fit nicely with all the other physics we know so far, but it doesn't seem implausible to me that there could be some fractions of the planck unit or that merely in the wide majority of cases anything under that granularity isn't likely to have any easily discernable physical effects about the planck unit scale (measuring anything at that scale would obviously be a tremendous challenge, if not impossible).