Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous measuring' of the open system by its environment induces decoherence of its wave function and entropy increase. Examples of nonrelativistic quantum Brownian motion and of interacting scalar elds illustrate these general concepts. It is shown that the Hartree-Fock approximation around the bare ( h = 0) classical limit can lead to

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... semiquantum chaos, which m a y aect the determination of entropy production and thermalization also in other cases.