Suppose Landau level degeneracy is $10^9$, if we force to put ($10^9+1$) particles on the level, what extra energy will we gain? (ignore particles interactions) Like electron degeneracy pressure, degeneracy energy in the white dwarf starts.
Incompressibility says the extra energy would be infinite if we force to do that, right?
Now suppose we decrease B field infinitesimally, so the calculated degeneracy is ($10^9-0.000000001$). Because there is not enough room for $10^9$ particles, there must be one particle jump to the next level and gain a finite energy. This is the statement of incompressibility.
It seems unfair for the particle to jump to next level, just due to 0.000000001 lack of room. Shouldn't we compare the Landau energy gap with certain "degeneracy energy" ?