  We consider asymptotic observables in quantum field theories in which the
S-matrix makes sense. We argue that in addition to scattering amplitudes, a
whole compendium of inclusive observables exists where the time-ordering is
relaxed. These include expectation values of electromagnetic or gravitational
radiation fields as well as out-of-time-order amplitudes. We explain how to
calculate them in two ways: by relating them to amplitudes and products of
amplitudes, and by using a generalization of the LSZ reduction formula. As an
application, we discuss one-loop master integrals contributing to gravitational
radiation in the post-Minkowski expansion, emphasizing the role of classical
cut contributions and highlighting the different infrared physics of in-in
observables.
