The Vlasov equation embodies the smooth-field approximation of the self-consistent equation of motion for charged-particle beams. This framework is fundamentally altered if we include the fluctuating forces that originate from the actual charge granularity. We thereby perform the transition from a reversible description to a statistical mechanics’ description covering also the irreversible aspects of beam dynamics. It will be shown that the macroscopic effects due to the fluctuating forces scale with two distinct quantities: the magnitude of the fluctuating forces, and the system’s temperature anisotropy. These analytical results are used to obtain a quantitative description for the effect of intrabeam scattering. ©2001 American Institute of Physics.