Transition from quantum to classical information in a superfluid

Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a ''quantum entropy'' 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 result illustrates the different roles that weakly interacting particles as photons vs. the particles in quantum fluids such as He4, He3, or XY ferromagnets might play in quantum information processes. In the context of regarding spacetime as a quantum superfluid our result provides a natural explanation why under ordinary circumstances physics is described by classical equations