In Hamiltonian mechanics, the Boltzmann equation is often written more generally as L ^ ^ [ f ] = C [ f ] , where L is the Liouville operator (there is an inconsistent definition between the Liouville operator as defined here and the one in the article linked) describing the evolution of a phase space volume and C is the collision operator. The non-relativistic form of L is L ^ ^ N R = ∂ ∂ ∂ ∂ t + p m ⋅ ⋅ ∇ ∇ + F ⋅ ⋅ ∂ ∂ ∂ ∂ p .