Vanishing center-of-mass diffusion for the three-dimensional FENE dumbbell model

We study the zero center-of-mass diffusion limit for the full kinetic FENE dumbbell model on the three-dimensional torus. For every solvent viscosity $\nu>0$, FENE exponent $k>2$, smooth divergence-free initial velocity, and smooth normalized initial density with bounded positive Maxwellian quotient, we select global positive-diffusion weak solutions converging to a global weak solution of the identical nondiffusive system. Velocity converges strongly in $L^2$ and polymer density and stress converge strongly in $L^1$ on finite time intervals. All transport and configuration fluxes have their original constitutive forms in the limit. The proof conditions on a spatial Brownian motion common to every polymer configuration. Nonlinear configuration entropies are transformed before expectation, giving only a linear spatial diffusion term. Conditional stress cutoffs, a transported limiting normalizer, and a joint covariance estimate then propagate a zero entropy defect without assuming strong convergence of the velocity gradient.