# 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:

- Russian Academy of Sciences (RAS), Moscow (Russian Federation). L.D. Landau Inst. for Theoretical Physics; Federal Inst. of Technology, Zurich (Switzerland). Theoretische Physik
- Federal Inst. of Technology, Zurich (Switzerland). Theoretische Physik
- Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division
- 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. Mon .
"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 = {Mon Sep 12 00:00:00 EDT 2016},

month = {Mon Sep 12 00:00:00 EDT 2016}

}

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