The third law of thermodynamics in open quantum systems
Abstract
In this work, we consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, S(T) → 0 as T → 0, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that S(T) → g ln 2 as T → 0, where g is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy S(x;T)→0 as T(x) → 0, except for cases of measure zero arising due to localized states, where T(x) is the temperature measured by a local thermometer.
- Authors:
-
[3]
- Univ. of Arizona, Tucson, AZ (United States); Univ. of Toronto, ON (Canada)
- Univ. of Arizona, Tucson, AZ (United States); Univ. of California, San Diego, CA (United States)
- Univ. of Arizona, Tucson, AZ (United States)
- Publication Date:
- Research Org.:
- Univ. of Arizona, Tucson, AZ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1610889
- Alternate Identifier(s):
- OSTI ID: 1557022
- Grant/Contract Number:
- SC0006699
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 151; Journal Issue: 6; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Chemistry; Physics
Citation Formats
Shastry, Abhay, Xu, Yiheng, and Stafford, Charles A. The third law of thermodynamics in open quantum systems. United States: N. p., 2019.
Web. doi:10.1063/1.5100182.
Shastry, Abhay, Xu, Yiheng, & Stafford, Charles A. The third law of thermodynamics in open quantum systems. United States. https://doi.org/10.1063/1.5100182
Shastry, Abhay, Xu, Yiheng, and Stafford, Charles A. Tue .
"The third law of thermodynamics in open quantum systems". United States. https://doi.org/10.1063/1.5100182. https://www.osti.gov/servlets/purl/1610889.
@article{osti_1610889,
title = {The third law of thermodynamics in open quantum systems},
author = {Shastry, Abhay and Xu, Yiheng and Stafford, Charles A.},
abstractNote = {In this work, we consider open quantum systems consisting of a finite system of independent fermions with arbitrary Hamiltonian coupled to one or more equilibrium fermion reservoirs (which need not be in equilibrium with each other). A strong form of the third law of thermodynamics, S(T) → 0 as T → 0, is proven for fully open quantum systems in thermal equilibrium with their environment, defined as systems where all states are broadened due to environmental coupling. For generic open quantum systems, it is shown that S(T) → g ln 2 as T → 0, where g is the number of localized states lying exactly at the chemical potential of the reservoir. For driven open quantum systems in a nonequilibrium steady state, it is shown that the local entropy S(x;T)→0 as T(x) → 0, except for cases of measure zero arising due to localized states, where T(x) is the temperature measured by a local thermometer.},
doi = {10.1063/1.5100182},
journal = {Journal of Chemical Physics},
number = 6,
volume = 151,
place = {United States},
year = {2019},
month = {8}
}
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Figures / Tables:
FIG. 1: Entropy S of an open quantum system consisting of a benzene ring coupled to an equilibrium electron reservoir, plotted as a function of the chemical potential μ of the reservoir for several temperatures. The molecule is modeled using Hückel theory (tight-binding approximation, see Appendix B), and energies aremore »
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Works referencing / citing this record:
Special topic on dynamics of open quantum systems
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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.