If we have an isolated system $Sb$ with thermodynamic entropy $Eb=X$ (and growing by the 2nd law of thermodynamics),
we could define an abstract system $Sa$ (containing the system $Sb$) but define the possible microstates as a single bit, being 1 (one) when $Eb>=X$, and 0 (zero) when $Eb < X$.
The microstate will tend to be $1$, so the entropy of the system $Sa$ tends to zero.
Eb = - k [p0 * log (p0) + p1 * log (p1)] --> 0
How could it be possible that an isolated system have a decreasing entropy?
Does the growth (or lack of growth) of the entropy depend on the microstates choosen?
Finally, if there is a restriction on how to choose the definition of the microstates, then what is that restriction?