Order preservation for the linear Boltzmann equation ($f_{1,0}\ge f_{2,0}⟹f_{1,t}\ge f_{2,t}$)

Nonnegative gain kernels and positive damping preserve pointwise order. The Volterra series for the linear Boltzmann equation has nonnegative terms when its initial datum is nonnegative. Applying this to the difference of two solutions proves comparison, with uniqueness identifying that difference with the positive series. This order property is distinct from positivity of a quadratic form on a Hilbert space.