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Title: 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:
 [1];  [2]; ORCiD logo [3]
  1. Univ. of Arizona, Tucson, AZ (United States); Univ. of Toronto, ON (Canada)
  2. Univ. of Arizona, Tucson, AZ (United States); Univ. of California, San Diego, CA (United States)
  3. 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. https://doi.org/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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Cited by: 2 works
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Figures / Tables:

FIG. 1 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 » expressed in units of the nearest-neighbor hybridization t. (a) Generic open system with Γ11 = t and all other matrix elements of Γ zero, illustrating the effect of the localized states at μ/t = ±1. (b) Fully open quantum system with Γ = (t/6)𝟙, illustrating the strong form of the third law, S(T)→ 0 as T → 0 ∀ μ.« less

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    Works referencing / citing this record:

    Special topic on dynamics of open quantum systems
    journal, January 2020

    • Berkelbach, Timothy C.; Thoss, Michael
    • The Journal of Chemical Physics, Vol. 152, Issue 2
    • DOI: 10.1063/1.5142731

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