Let ∂ ∂ Ω Ω move with a flow velocity u n and let particles inside Ω Ω have velocities v . Let n be the unit outward normal to the surface ∂ ∂ Ω Ω . Let ρ ρ be the density of matter in the region, q ¯ ¯ be the entropy flux at the surface, and r be the entropy source per unit mass. Then the entropy inequality may be written as