skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: H-theorem in quantum physics

Abstract

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.

Authors:
 [1];  [2];  [3];  [4];  [3]
  1. Russian Academy of Sciences (RAS), Moscow (Russian Federation). L.D. Landau Inst. for Theoretical Physics; Federal Inst. of Technology, Zurich (Switzerland). Theoretische Physik
  2. Federal Inst. of Technology, Zurich (Switzerland). Theoretische Physik
  3. Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
  4. Moscow Inst. of Physics and Technology (MIPT), Moscow (Russian Federation)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
Swiss National Science Foundation (SNSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1352603
Grant/Contract Number:
AC02-06CH11357; 14-02-01287
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Scientific Reports
Additional Journal Information:
Journal Volume: 6; Journal Issue: 1; Journal ID: ISSN 2045-2322
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Lesovik, G. B., Lebedev, A. V., Sadovskyy, I. A., Suslov, M. V., and Vinokur, V. M. H-theorem in quantum physics. United States: N. p., 2016. Web. doi:10.1038/srep32815.
Lesovik, G. B., Lebedev, A. V., Sadovskyy, I. A., Suslov, M. V., & Vinokur, V. M. H-theorem in quantum physics. United States. doi:10.1038/srep32815.
Lesovik, G. B., Lebedev, A. V., Sadovskyy, I. A., Suslov, M. V., and Vinokur, V. M. 2016. "H-theorem in quantum physics". United States. doi:10.1038/srep32815. https://www.osti.gov/servlets/purl/1352603.
@article{osti_1352603,
title = {H-theorem in quantum physics},
author = {Lesovik, G. B. and Lebedev, A. V. and Sadovskyy, I. A. and Suslov, M. V. and Vinokur, V. M.},
abstractNote = {Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.},
doi = {10.1038/srep32815},
journal = {Scientific Reports},
number = 1,
volume = 6,
place = {United States},
year = 2016,
month = 9
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

Save / Share:
  • EPR locality is discussed from the point of view of determinism. (AIP)
  • The principle of EPR locality is discussed. (AIP) e
  • A locality property expressing the idea that causal influences can propagate only forward in time, from earlier cause to later effect, and no faster than light is shown to be mathematically incompatible with certain predictions of quantum theory. The contradiction is proved without invoking any additional assumptions such as realism or hidden variables that contravene conventional quantum thinking. The failure of this locality property refines ideas about the theory of relativity, and opens the way to an objective interpretation of quantum theory that may expand its domain of applicability outside the one circumscribed by the orthodox Copenhagen interpretation.
  • We consider the quantum mechanical generalization of Crooks Fluctuation and Jarzynski Equality Theorem for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.
  • For the largest class of physical systems having a classical analog, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given, in terms of a notion of regularized action function. As a consequence of the study of the symmetries of this action, an associated Noether theorem is obtained. All the quantum symmetries resulting from the canonical quantization procedure follow in this way, as well as a number of symmetries which are new even for the case of the simplest systems. The method is based on the study of a corresponding Lie algebra and an analytical continuationmore » in the time parameter of the probabilistic construction given in paper I of this work. Generically, the associated quantum first integrals are time dependent and the probabilistic model provides a natural interpretation of the new symmetries. Various examples illustrate the physical relevance of our results.« less