Geodesic
Using the~Renyi entropy to describe quantum dissipative systems in
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 444-453

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We develop a formalism for describing quantum dissipative systems in statistical mechanics based on the quantum Renyi entropy. We derive the quantum Renyi distribution from the principle of maximum quantum Renyi entropy and differentiate this distribution (the temperature density matrix) with respect to the inverse temperature to obtain the Bloch equation. We then use the Feynman path integral with a modified Mensky functional to obtain a Lindblad-type equation. From this equation using projection operators, we derive the integro-differential equation for the reduced temperature statistical operator, an analogue of the Zwanzig equation in statistical mechanics, and find its formal solution in the form of a series in the class of summable functions.
Keywords: quantum Renyi entropy, quantum Renyi distribution, Bloch equation for quantum Renyi distribution, Lindblad equation, quantum dissipative system.
Mots-clés : Zwanzig equation 
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     author = {V. S. Kirchanov},
     title = {Using {the~Renyi} entropy to describe quantum dissipative systems in},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {444--453},
     publisher = {mathdoc},
     volume = {156},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a8/}
}
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V. S. Kirchanov. Using the~Renyi entropy to describe quantum dissipative systems in. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 444-453. http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a8/