Toward a quantum generalization of equilibrium statistical thermodynamics: ħ-k Dynamics

• Published in: Theoretical and mathematical physics Vol. 160; no. 2; pp. 1177 - 1189
• Main Authors: Sukhanov, A. D., Golubeva, O. N.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-08-2009
• Subjects: Applications of Mathematics; Mathematical and Computational Physics; Physics; Physics and Astronomy; Theoretical; dynamics; stochastic action operator; quantum thermal bath; cold vacuum; effective action; thermal vacuum; quantum-thermal entropy
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1007/s11232-009-0109-0

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 ħ-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.