On Boltzmann's $H$-theorem
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 3, pp. 425-429

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Sufficient conditions are found directly for a quantum dynamical system on the basis of which a proof of Boltzmann's $H$-theorem is given. At the same time it is shown that in the general case for sufficiently long times (near equilibrium) the entropy production is of variable sign.
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     author = {L. A. Khalfin},
     title = {On {Boltzmann's} $H$-theorem},
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     year = {1978},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_3_a16/}
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L. A. Khalfin. On Boltzmann's $H$-theorem. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 3, pp. 425-429. http://geodesic.mathdoc.fr/item/TMF_1978_35_3_a16/