Decoherence and entropy of primordial fluctuations. II. The entropy budget

We calculate the entropy of adiabatic perturbations associated with a truncation of the hierarchy of Green functions at the first nontrivial level, i.e. in a self-consistent Gaussian approximation. We derive the equation governing the entropy growth and discuss its phenomenology. It is parametrized by two model-dependent kernels. We then examine two particular inflationary models, one with isocurvature perturbations, the other with corrections due to loops of matter fields. In the first model the entropy grows rapidly, while in the second the state remains pure (at one loop).