In statistical mechanics the entropy of a macroscopic system in equilibrium, assuming equipartition, is equal to the logarithm of the number of microstate compatible with it, up to a fixed and well-defined constant. This coincides with the traditional definition of the entropy (which is where the constant comes from).
This definition should be independent of the underlying theory, but how is that possible? When substructure is considered or discovered (e.g. of particles in a gas), or when theories are replaced or refined, the number of microstates (according to the theory) will generally change. It doesn't seem to be the case however that the absolute entropy can not be computed unless a complete theory of every detail of the system is known. Moreover entropy is something that can be measured without having any idea of theory or substructure.
Finally many or most systems have an infinite state space, for example a classical many-particle macrostate will correspond to an infinite subset of the phase space, and an ideal quantum gas at sufficiently high temperature/energy so that unbounded states are accessible will correspond to an infinite dimensional subspace of its Hilbert space. How would this (i.e. the counting of states) work there?
Without a doubt this is a very naive question, but i really have no idea of what the answer could be.