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Title: Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law

Abstract

In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantummore » Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. As a result, entropy and entanglement will be the main theme of our second paper on this subject matter.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [4]
  1. Fudan Univ., Shanghai (China). Center for Field Theory and Particle Physics
  2. National Cheng Kung Univ., Tainan (Taiwan). Dept. of Physics
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Fudan Univ., Shanghai (China). Center for Field Theory and Particle Physics; Univ. of Maryland, College Park, MD (United States). Maryland Center for Fundamental Physics and Joint Quantum Inst. (JQI)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1419751
Alternate Identifier(s):
OSTI ID: 1417775
Report Number(s):
LA-UR-17-21711
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1801385
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Brownian motion; Brownian dynamics; open quantum systems; quantum thermodynamics; dissipative particle dynamics; Langevin equation; non-Markovian processes; nonequlibrium Green's function; path-integral methods; quantum field theory; second quantization

Citation Formats

Hsiang, Jen -Tsung, Chou, Chung Hsien, Subasi, Yigit, and Hu, Bei Lok. Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.97.012135.
Hsiang, Jen -Tsung, Chou, Chung Hsien, Subasi, Yigit, & Hu, Bei Lok. Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law. United States. doi:10.1103/PhysRevE.97.012135.
Hsiang, Jen -Tsung, Chou, Chung Hsien, Subasi, Yigit, and Hu, Bei Lok. Tue . "Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law". United States. doi:10.1103/PhysRevE.97.012135. https://www.osti.gov/servlets/purl/1419751.
@article{osti_1419751,
title = {Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law},
author = {Hsiang, Jen -Tsung and Chou, Chung Hsien and Subasi, Yigit and Hu, Bei Lok},
abstractNote = {In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. As a result, entropy and entanglement will be the main theme of our second paper on this subject matter.},
doi = {10.1103/PhysRevE.97.012135},
journal = {Physical Review E},
number = 1,
volume = 97,
place = {United States},
year = {2018},
month = {1}
}

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Cited by: 4 works
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Figures / Tables:

Fig. 1 Fig. 1: We compare the difference in predictions from the equilibrium and nonequilibrium approaches. The blue (solid) curve describes the temperature dependence of the mechanical energy of the oscillator in the equilibrium thermal state. The other two curves give the temperature variations of the mechanical energy of the oscillator whichmore » interacts with a bath that is initially in the thermal state. As an illustration of the nontrivial effect in the choice of the cutoff scale, these two curves have different cutoff scales.« less

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    Works referencing / citing this record:

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    Steady-state entanglement and coherence of two coupled qubits in equilibrium and nonequilibrium environments
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      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.