Abstract
We extend the Zwanzig projector formalism to coupled systems taking into account the mutual interactions of the reduced density matrices of both systems. In the Born- and Markoff-approximation we end up with a bilinear masterequation for occupation probabilities, in contrast to the usually studied linear equations. We derive theH-theorem for this equation and show that the stationary solution is the canonical or more generally a grand canonical density matrix.
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For interesting discussions we wish to thank Professors F. Haake, R. Bonifacio, Dr. P. Schwendimann and P. Talkner.
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Grabert, H., Weidlich, W. Masterequation,H-theorem and stationary solution for coupled quantum systems. Z. Physik 268, 139–143 (1974). https://doi.org/10.1007/BF01669871
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DOI: https://doi.org/10.1007/BF01669871