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 Quantum Theory of Irreversibility

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A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the Liouville-von Neumann equation describing the evolution of a density super- operator, it is demonstrated that the entropy production for an isolated system is non-negative, which provides an arrow of time. Moreover, following the procedure of non-equilibrium thermodynamics a master matrix is introduced for which a mi- croscopic expression is obtained. Then, the quantum Boltzmann equation is derived in terms of a transition superoperator related to that master matrix.

Author: A. Perez-Madrid

Source: https://archive.org/

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