Brownian yet non-Gaussian diffusion through equilibrium nonlinear friction

What the math gives to ML

The paper provides a constructive fluctuation-dissipation mechanism for Brownian yet non-Gaussian motion: velocity-dependent friction must be paired with velocity-dependent diffusion according to B(v) = lambda(v) k_B T. This preserves a Gaussian equilibrium velocity distribution while producing non-Gaussian displacement statistics at intermediate times and ordinary diffusion asymptotically. A transferable neural-network construction is a momentum optimizer with nonlinear, state-dependent friction and matched noise, including the drift correction required by the Fokker-Planck operator. The key falsifiable prediction is that matched dynamics preserve the target stationary momentum law, while mismatched friction and noise produce a measurable variance and kurtosis error.