The Mathematical Structure of Superspace as a Consequence of Time   Asymmetry
  It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields directly to an irreversible evolution, in the classical (and semiclassical) phase of the universe, where:   Decoherence and correlations take place and therefore give origin to a classical universe. The second law of thermodynamic is demonstrated. Connection with Reichenbach branch system idea can be implemented. Some rough coincidence with observational data are obtained. The arrows of time can be correlated. Time asymmetry can be explained as a state space asymmetry (e. g. like a spontaneous symmetry breaking All these facts solve the problem of time-asymmetry and show that it is time asymmetry itself that defines the most important features of mathematical structure of superspace. 
Mario Castagnino