We have discussed in considerable detail a microscopic quantum mechanical model for a laser cavity coupled to different reservoirs and have given a precise sense in which the laser shows irreversible classical and stochastic behavior in the thermodynamic limit. We have, however, only barely prodded the sleeping giant of nonequilibrium statistical mechanics. There are many open problems in this field, both of a technical and conceptual nature. There is the immediate question, whether the choice of the reservoirs, in particular the use of regular Hamiltonians and nonlinear couplings, can qualitatively change the phase transition in this class of mean field models. A nontrivial generalization of our approach is necessary in order to treat the finite mode laser. Our results on the intensive and fluctuation observables are the first two terms in an asymptotic expansion for large finite lasers. It is not clear how good this expansion is, if one is interested in the equilibrium properties of the finite nonlinear system for t→∞. Hopefully, the two limits, N→∞ and t→∞, can be exchanged for certain observables away from threshold. Finally, it is clear that the really hard problems of irreversible statistical mechanics are not the construction of quantum mechanical cuckoo clocks but the understanding of continuous systems with short range and Coulomb forces.
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