Entropy Chaos and Bose-Einstein Condensation

We prove the entropy-chaos property for the system of N indistinguishable interacting diffusions rigorously associated with the ground state of N trapped Bose particles in the Gross-Pitaevskii scaling limit of infinitely many 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-Pitaevkii functional.