  A stochastic approach to the (generic) mean-field limit in Bose-Einstein
Condensation is described and the convergence of the ground state energy as
well as of its components are established. For the one-particle process on the
path space a total variation convergence result is proved. A strong form of
Kac's chaos on path-space for the $k$-particles probability measures are
derived from the previous energy convergence by purely probabilistic techniques
notably using a simple chain-rule of the relative entropy. The Fisher's
information chaos of the fixed-time marginal probability density under the
generic mean-field scaling limit and the related entropy chaos result are also
deduced.
