The abstract theory concerns the mathematical convergence of microscopic dynamical systems described by Newtonian laws to macroscopic statistical models governed by the Boltzmann equation over long time scales, resolving Hilbert's sixth problem in gas dynamics. This theoretical framework establishes rigorous bounds on particle collision histories and recollisions within an infinite limit system (Boltzmann-Grad limit), utilizing graph-theoretic estimates of diagrammatic expansions to validate the emergence of continuum equations from discrete mechanics. The domain belongs to mathematical physics, specifically statistical mechanics and kinetic theory, where it defines the validity boundaries for deriving macroscopic thermodynamic properties from fundamental microscopic laws without relying on probabilistic averaging that fails at long durations due to chaotic particle interactions.
The abstract theory concerns the mathematical convergence of microscopic dynamical systems described by Newtonian laws to macroscopic statistical models governed by the Boltzmann equation over long t…