Quantitative propagation of chaos on arbitrary finite time intervals for the three-dimensional repulsive Vlasov-Poisson-Fokker-Planck equation

We prove quantitative propagation of chaos in total variation for repulsive Vlasov--Riesz--Fokker--Planck (VRFP) equations on Tᵈ and Rᵈ with unregularized interaction potentials with singularity |x|⁻ˢ, $03$ gives convergence to the global classical solution on every finite time interval. The proof combines conditioning of the initial product law with weighted BBGKY estimates. A decomposition of the potential and a bounded modification of the far-field force yield weighted bounds growing geometrically in the marginal order on the prescribed interval. A centered second-moment estimate permits summation of the error hierarchy, and a synchronous coupling transfers the estimate to the original dynamics.