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Kinetic limits and fluctuations over the Boltzmann lifespan
Derives the nonlinear Boltzmann equation from three-dimensional grand-canonical Newtonian gases throughout every regular kinetic interval with uniform Gaussian decay. Stable finite-range radial potentials may have attractive wells and a singular repulsive core; initial pair exclusion and spatially summable Gaussian density and gradient bounds are assumed. A companion gives finite-dimensional hard-sphere Gaussian fluctuations, centered at the exact microscopic expectation and governed by the linear fluctuating Boltzmann equation.
Manuscripts in this family · 2
The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals
Sep 23, 2026·paper.pdf
We derive the nonlinear Boltzmann equation from a grand-canonical Newtonian gas with initial pair exclusion. We treat stable, finite-range radial potentials that are C except for an allowed repulsive singularity at the origin, and C initial probability densities with spatially summable Gaussian bounds on the density and its spatial gradient. All fixed-order rescaled factorial marginals converge in L, uniformly throughout every finite interval on which the classical kinetic solution has a uniform Gaussian bound. The result allows attractive wells and dynamically formed clusters, without restrictions on the differential scattering cross-section.
Hard-sphere fluctuations on the regular Boltzmann lifespan
Sep 23, 2026·paper.pdf
We prove a finite-dimensional central limit theorem away from equilibrium for a deterministic grand-canonical hard-sphere gas in three dimensions. The initial probability density is smooth, with spatially summable Gaussian velocity bounds on the density and its spatial gradient. The limit holds on every finite interval on which the classical Boltzmann solution has uniform Gaussian velocity decay. The empirical measure is centered by its exact microscopic expectation. Its fluctuations converge to the Gaussian solution of the linear fluctuating Boltzmann equation.