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

Journal Article · 22 January 2018 · Physical Review E

DOI: https://doi.org/10.1103/PhysRevE.97.012135 · OSTI ID:1419751

Hsiang, Jen -Tsung ^[1]; Chou, Chung Hsien ^[2]; Subasi, Yigit  ^[3]; Hu, Bei Lok ^[4]

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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)

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1419751
• Report Number(s): LA-UR--17-21711
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 1 Vol. 97; ISSN PLEEE8; ISSN 2470-0045
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English