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Theories which have fundamental information destruction or decoherence are motivated by the black hole information paradox where one appears to have pure states evolving into mixed states.
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For a review, see for example, Quantum Dynamical Semigroups and Applications, R. Alicki and K. Lendi, Springer (2007), and The Theory of Open Quantum Systems, H.-P. Breuer and F. Petruccione, Oxford University Press (2002)
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