  We prove the entropy-chaos property for the system of N undistinguishable
interacting diffusions rigorously associated with the ground state of N trapped
Bose particles in the Gross-Pitaevskii scaling limit of infinite particles. On
the path-space we show that the sequence of probability measures of the
one-particle interacting diffusion weakly converges to a limit probability
measure, uniquely associated with the minimizer of the Gross-Pitaevskii
functional.
