Why is there an absolute entropy? Given any non-discrete probability distribution, we don't really have an absolute entropy because the entropy depends on the parametrization of the distribution (e.g. Beta vs. Beta-prime) which was arbitrarily chosen. Another way to put it is that instead of entropies we only have Kullback–Leibler (KL) divergences aka relative entropies. So, why isn't there a physics analogue to KL-divergence? Just as we have relativistic velocity, which has some properties, why don't we also have relative entropies, which have some properties? Instead of saying the absolute entropy of the universe increases, why don't we say that the relative entropy given our prior belief of the universe increases?
Alternatively, what is the relation between entropy and number of microstates when the physical system is continuous, and how do we "count microstates"?