 In 1945 Prigogine (see also Prigogine (1947)) proposed a “Theorem of Minimum Entropy Production” which applies only to the purely diffusive linear regime, with negligible inertial terms, near a stationary thermodynamically non-equilibrium state.Prigogine's proposal is that the rate of entropy production is locally minimum at every point.The proof offered by Prigogine is open to serious criticism.