Typically one thinks of the sources as being at infinite past, and the detection at infinite future; then a reversible S-matrix description applies.
For photons, a corresponding treatment of sources and detectors can be found in Mandel & Wolf's treatise on quantum optics. But their treatment doesn't give any hint on irreversibility.
[Edit] Detection is always irreversible; nothing counts as detected unless there is an irreversible record of it. There is no really good account from first principles how an irreversible detection event is achieved. From the 1999 article ''Some problems in statistical mechanics that I would like to see solved'' by Elliot Lieb
The measurement process in quantum mechanics is not totally understood, even after three quarters of a century of thought by the deepest thinkers. At some level, the problems of quantum mechanical measurement are related, distantly perhaps, to the problems of non-equilibrium statistical mechanics. Several models (e.g. the laser) indicate this, but the connection, if any, is unclear and I would like to see more light on the subject.
A field theoretic discussion of irreversibility necessitates a statistical mechanics treatment. This more detailed modeling is done in practice in a hydrodynamic or kinetic approximation. They treat sources as generators of beams with an extended distribution in space or phase space, respectively.
The dynamics of both descriptions is irreversible, and may be computed in terms of $k$-particle irreducible ($k$PI) Feynman diagrams for $k=1$ and $k=2$, respectively.
The kinetic description is based on the Kadanoff-Baym equations in the 2PI Schwinger-Keldysh (CTP) formalism. The Kadanoff-Baym equations are dynamical equations for the 2-particle Wightman functions and their ordered analoga, and are used in practice to model high energy heavy ion collision experiments. See, e.g.,
and the discussions in
Good reading on the Keldysh formalism
What is known about quantum electrodynamics at finite times?
The hydrodynamic description is based on the simpler 1PI approach, but it is
(to my knowledge) used mainly theoretically; see, e.g.,
This post imported from StackExchange Physics at 2015-08-01 13:49 (UTC), posted by SE-user Arnold Neumaier
Reviews of Modern Physics 49, 435 (1977)
and the papers