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 [Formula: see text]-particles probability measures is derived from the previous energy convergence by purely probabilistic techniques notably using a simple chain-rule of the relative entropy. 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.

中文翻译：

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平均场玻色-爱因斯坦凝聚中的强 Kac 混沌

描述了玻色-爱因斯坦凝聚中（通用）平均场极限的随机方法，并建立了基态能量及其分量的收敛。对于路径空间上的单粒子过程，证明了全变分收敛结果。[公式：见文本]-粒子概率度量的路径空间上的 Kac 混沌的一种强形式是通过纯概率技术，特别是使用相对熵的简单链式法则，从先前的能量收敛推导出来的。还推导了一般平均场尺度限制下固定时间边际概率密度的Fisher信息混沌及其相关熵混沌结果。