Probability space of wave functions

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Abstract
The entropy maximization and the divergence minimization, two related optimization techniques coming from standard statistical mechanics and often applied nowadays to probabilistic modeling, are used here together in order to organize the space of wave functions as a probability space when the only available information on the quantum system at the initial moment is the density matrix, which describes the mean behavior of a quantum ensemble. The Schroumldinger equation determines a nonconservative flow in this probability space transforming the independent Gaussian product measure, at the initial moment, into a dependent Gaussian product measure at an ulterior moment. Such a transformation can be viewed as a generalization of the Liouville theorem from classical statistical mechanics.

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