Convexity of θ θ ( λ λ ) gives the sufficient and necessary conditions for the proper dissipation inequality: d F d t < 0 if and only if θ θ ( λ λ ) < θ θ ( 1 ) for some λ λ < 1 ; d F d t ≤ ≤ 0 if and only if θ θ ( λ λ ) ≤ ≤ θ θ ( 1 ) for some λ λ < 1.