Quantum theory of irreversibility |
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Authors: | A Pérez-Madrid |
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Institution: | Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain |
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Abstract: | A generalization of the Gibbs–von Neumann entropy is proposed based on the quantum BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy as the non-equilibrium entropy for an N-body system. By using a generalization of the Liouville–von Neumann equation describing the evolution of a density superoperator, the entropy production for an isolated system is calculated, being non-zero in general. The existence of a non-zero entropy production allows us, following the procedure of non-equilibrium thermodynamics to introduce a master matrix for which a microscopic expression is obtained. After this, as a test of our theory the quantum Boltzmann equation is derived in terms of a transition superoperator related to this master matrix. |
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Keywords: | Quantum statistical mechanics Non-equilibrium and irreversible thermodynamics Kinetic and transport theory of gases |
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