This equation sets the action of the Liouville operator equal to that of the collision operator.
In quantum field theory, this equation is generalized by the Kadanoff-Baym equations. Deviations from ideality are commonly represented by the Shan-Chen pseudopotential in lattice methods for solving this equation under the BGK approximation. First-order perturbative expansion of this equation in terms of the Knudsen number produces the Navier-Stokes equations via the Chapman-Enskog method. In Gouy-Chapman theory, this equation is used to calculate the local density of counter-ions and then substituted into the (*) Poisson equation. This equation sets the action of the Liouville operator equal to that of the collision operator. For 10 points, name this central equation of non-equilibrium statistical mechanics that describes the evolution of a system's particle distribution function and directly implies its namesake physicist's H-theorem.
In quantum field theory, this equation is generalized by the Kadanoff-Baym equations.
Boltzmann transport equation