2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138209A systematic expansion of the Boltzmann equation for the diffusion of dilute tracers, in powers of the Knudsen number, carried out to next-to-leading order (NLO), gives the relativistic causal diffusion equation (Kelly's equation). Using dimensionless combinations of dynamical quantities, we show when the small NLO term plays a crucially important role. We proceed to show that a derivation of Kelly's equation from a microscopic theory of the correlation function of the number density of diffusers is possible. The correlator fulfils the Green-Kubo relation for the diffusion constant, as well as an f-sum which goes beyond a purely phenomenological causal theory. We argue that the construction generalizes to the full hydrodynamic equations.5 pages, 1 figureNuclear TheoryHigh Energy Physics - PhenomenologyHigh Energy Physics - TheoryNuclear Experimenttext