Geodesic
Toward a quantum generalization of equilibrium statistical thermodynamics: $\hbar$–$k$ Dynamics
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 370-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that the quantum statistical mechanics (QSM) describing the quantum and thermal properties of objects only has the sense of a particular semiclassical approximation. We propose a more general microdescription than in QSM of objects in a thermal bath with the vacuum explicitly taken into account; we call it $\hbar$–$k$ dynamics. We construct a qualitatively new model of the object environment, namely, a quantum thermal bath. We study its properties including the cases of a "cold" and a "thermal" vacuum. We introduce the stochastic action operator and show its fundamental role in the microdescription. We establish that the corresponding macroparameter, the effective action, plays just as significant a role in the macrodescription. The most important effective macroparameters of equilibrium quantum statistical thermodynamics—internal energy, temperature, and entropy—are expressed in terms of this macroparameter.
Keywords: $\hbar$–$k$ dynamics, quantum thermal bath, cold vacuum, thermal vacuum, stochastic action operator, effective action, quantum-thermal entropy. 
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     author = {A. D. Sukhanov and O. N. Golubeva},
     title = {Toward a~quantum generalization of equilibrium statistical thermodynamics: $\hbar${\textendash}$k$ {Dynamics}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a9/}
}
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A. D. Sukhanov; O. N. Golubeva. Toward a quantum generalization of equilibrium statistical thermodynamics: $\hbar$–$k$ Dynamics. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 370-384. http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a9/

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