Given a function f d d t f = ∂ ∂ ∂ ∂ t f + { f , H } , if there is a probability distribution ρ, then (since the phase space velocity ( p ˙ ˙ i , q ˙ ˙ i ) has zero divergence and probability is conserved) its convective derivative can be shown to be zero and so ∂ ∂ ∂ ∂ t ρ ρ = − − { ρ ρ , H }