  Whereas the entropy of any deterministic classical system described by a
principle of least action is zero, one can assign a "quantum information" to
quantum mechanical degree of freedom equal to Hausdorff area of the deviation
from a classical path. This raises the question whether superfluids carry
quantum information. We show that in general the transition from the classical
to quantum behavior depends on the probing length scale, and occurs for
microscopic length scales, except when the interactions between the particles
are very weak. This transition explains why, on macroscopic length scales,
physics is described by classical equations.
