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,
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