We introduce a modulated Gibbs measure for the usual tensorized initial data for stochastic Newton's systems with singular repulsive interactions. Using the uniform-in-$N$ partition-function estimates of Wang--Zhao \cite{wang2026uniform}, we show that the modulated Gibbs measure and its tensorized reference are $O(N^{-1})$-close in normalized relative entropy. A stability argument then transfers propagation of chaos from modulated Gibbs measures to tensorized data and other initial laws at the same entropy scale. Combined with the weighted BBGKY estimates of Bresch--Jabin--Soler \cite{bresch2025new}, this yields the first cutoff-free mean-field limit and propagation of chaos for the three-dimensional Vlasov--Poisson--Fokker--Planck (VPFP) equation on an $N$-independent short-time interval.
We prove quantitative propagation of chaos in total variation for repulsive Vlasov--Riesz--Fokker--Planck (VRFP) equations on $\mathbb{T}^d$ and $\mathbb{R}^d$ with unregularized interaction potentials with singularity $|x|^{-s}$, $0<s<d/2$. On every finite time interval on which the limiting classical solution satisfi...
We prove nonlinear Landau damping for the two-dimensional Vlasov--Poisson system in the unconfined Euclidean setting near the homogeneous Poisson equilibrium \[ \mu(v)=\frac{1}{2\pi}(1+|v|^2)^{-3/2}. \] For small, smooth, localized, and neutral perturbations we establish global existence, quantitative pointwise decay e...
We study nonlinear Landau damping for the Vlasov--Yukawa equation in the large-box regime, as a periodic box of length $2\pi L$ expands to the whole space. First, for $d\ge 3$, we prove global stability and scattering in an $L$-dependent Gevrey class, with estimates uniform for $L\ge L_0$. The density obeys a two-regim...
We extend Mark Kac's kinetic framework from single-species Euclidean spaces to a two-species, non-linear interaction space on the open cone $(0, \infty)^2$ governed by the Matsumoto--Yor rational collision involution. We identify a non-linear conserved energy $E(x,y) = x + y + 1/x$ and an invariant conic metric measure...
We prove quantitative propagation of chaos in total variation for the unregularized repulsive Vlasov--Riesz--Fokker--Planck system on $\mathbb{T}^d$ and $\mathbb{R}^d$, $d\ge2$. For product initial data and potentials with singularity $|x|^{-s}$, $0<s<d/2$, we obtain an algebraic convergence rate for the $k$-particle m...
We study higher moments of quantum fluctuations and microscopic correlation energy in the three-dimensional Gross--Pitaevskii regime. For a smooth, compactly supported, nonnegative radial interaction and an $N$-independent normalized initial condensate wave function in $H^6$, we propagate the third spectral moment of a...
