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We derive quantitative estimates proving the propagation of chaos for largestochastic systems of interacting particles. We obtain explicit bounds on therelative entropy between the joint law of the particles and the tensorized lawat the limit. We have to develop for this new laws of large numbers at theexponential scale. But our result only requires very weak regularity on theinteraction kernel in the negative Sobolev space $\dot W^{-1,\infty}$, thusincluding the Biot-Savart law and the point vortices dynamics for the 2dincompressible Navier-Stokes.

Quantitative estimate of propagation of chaos for stochastic systems with $W^{-1, \infty}$ kernels