Minimal Irreversible Quantum Mechanics: Decoherence and classical equilibrium limit

Using the Minimal Irreversible Quantum Mechanics formalism, it is demonstrated that the quantum regime can be considered as the transient phase while the final classical equilibrium regime is the permanent state. A basis where exact matrix decoherence appears for these final states is found. The appearance of a classical universe in quantum gravity models is the cosmological version of this problem.