Model description of particle collisions in one-component systems

Linearized model collision operators that correctly describe the relaxation of the first 13 hydrodynamic moments in single-component systems are derived. For particles with Coulomb interaction potential, the calculations are made in the second Chapman–Enskog approximation. An expression for the intensity of the Langevin source in the kinetic equation is obtained in the same approximation. The Landau–Lifshitz formula is generalized to non-Markov processes. A new form of model collision operator for the particles of a Boltzmann gas of hard spheres is proposed.