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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 8, p.787-796
https://doi.org/10.15407/ujpe58.08.0787    Paper

Sukhanov A.D.1, Golubeva O.N.2, Bar’yakhtar V.G.3

1 Bogoliubov Laboratory of Theoretical Physics, Joint Institute of Nuclear Reaserch
(Dubna 141980, Russia; e-mail: ogol@oldi.ru)
2 Russian Peoples Friendship University
(Moscow, Russia; e-mail: ogol@mail.ru)
3 Institute of Magnetism,
Nat. Acad. of Sci. of Ukraine and Ministry of Education and Science, Youth and Sport of Ukraine
(36, Academician Vernadsky Blvd., Kyiv 03680, Ukraine; e-mail: victor.baryakhtar@gmail.com)

Quantum-Mechanical Analog of the Zeroth Law of Thermodynamics (to the Problem of Incorporating Thermodynamics into the Quantum-Mechanical Theory)

Section: General problems of theoretical physics
Original Author's Text: Russian

Abstract: The presented approach to incorporate the stochastic thermodynamics into the quantum theory is based on the idea, proposed earlier by the authors, to consistently consider the stochastic influence by the environment considered as the whole and described by the wave functions of arbitrary vacua. In this research, a possibility of the explicit incorporation of the zeroth law of stochastic thermodynamics into the quantum-mechanical theory in the form of the saturated Schr?odinger uncertainty relation is realized. This allows a comparative analysis between the sets of arbitrary vacuum states, namely, squeezed coherent (SCSs) and correlated coherent (CCSs) states, to be carried out. A possibility to establish a relation between SCSs and CCSs, on the one hand, and thermal states, on the other hand, is discussed.

Key words: uncertainty relation, thermal equilibrium, the zeroth law, invariance, squeezed coherent states, correlated coherent states.

References:

  1. A.D. Sukhanov and O.N. Golubeva, Elem. Chast. At. Yadra Pis'ma 9, 495 (2012).
  2. A.D. Sukhanov, O.N. Golubeva, and V.G. Bar'yakhtar, arXiv: quant-ph/1211.3017v1.
  3. H. Umezawa, Advanced Field Theory. Micro-, Macro-, and Thermal Physics (Amer. Inst. of Phys., New York, 1993).
  4. J.M. Park, arXiv: math-phys/0409008v1.
  5. E. Wigner and M.M. Yanase, Proc. Nat. Acad. Sci. USA 49, 910 (1963).
     https://doi.org/10.1073/pnas.49.6.910