In its most compact form, this equation sets the total derivative of a distribution equal to a collisional term, and if that collisional term is zero, this equation reduces to the Vlasov equation.
A common use of this equation is to derive the equation of change for mean values. Near equilibrium, the quantity of interest in this equation may be parametrized as deviating from the equilibrium state by a parameter phi. In that case, this equation reduces to an integral equation whose right hand side is an integral over volume and solid angle of the product of the change in phi, the equilibrium distribution, the perturbed distribution, and the velocity. One simplifying approximation useful in solving this equation is to assume that collisions serve to restore equilibrium; then one side of this equation can be written as the difference between the original and current distribution functions. In its most compact form, this equation sets the total derivative of a distribution equal to a collisional term, and if that collisional term is zero, this equation reduces to the Vlasov equation. For ten points, identify this equation which forms the basis of the theory of transport processes.
A common use of this equation is to derive the equation of change for mean values.
Boltzmann transport equation