By using the quasi-equilibrium Helmholtz energy, which is defined as the thermodynamic work in a quasi-static process, we investigate the thermal properties of both an isothermal process and a transition process between the adiabatic and isothermal states (adiabatic transition). Here, the work is defined by the change in energy from a steady state to another state under a time-dependent perturbation. In particular, the work for a quasi-static change is regarded as thermodynamic work. We employ a system–bath model that involves time-dependent perturbations in both the system and the system–bath interaction. We conduct numerical experiments for a three-stroke heat machine (a Kelvin–Planck cycle). For this purpose, we employ the hierarchical equations of motion (HEOM) approach. These experiments involve an adiabatic transition field that describes the operation of an adiabatic wall between the system and the bath. Thermodynamic–work diagrams for external fields and their conjugate variables, similar to the P–V diagram, are introduced to analyze the work done for the system in the cycle. We find that the thermodynamic efficiency of this machine is zero because the field for the isothermal processes acts as a refrigerator, whereas that for the adiabatic wall acts as a heat engine. This is a numerical manifestation of the Kelvin–Planck statement, which states that it is impossible to derive the mechanical effects from a single heat source. These HEOM simulations serve as a rigorous test of thermodynamic formulations because the second law of thermodynamics is only valid when the work involved in the operation of the adiabatic wall is treated accurately.
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7 July 2022
Research Article|
July 01 2022
The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach
Shoki Koyanagi
;
Shoki Koyanagi
(Data curation, Investigation, Methodology, Writing – original draft)
Department of Chemistry, Graduate School of Science, Kyoto University
, Kyoto 606-8502, Japan
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Yoshitaka Tanimura
Yoshitaka Tanimura
a)
(Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing)
Department of Chemistry, Graduate School of Science, Kyoto University
, Kyoto 606-8502, Japan
a)Author to whom correspondence should be addressed: tanimura.yoshitaka.5w@kyoto-u.jp
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a)Author to whom correspondence should be addressed: tanimura.yoshitaka.5w@kyoto-u.jp
J. Chem. Phys. 157, 014104 (2022)
Article history
Received:
March 29 2022
Accepted:
June 08 2022
Citation
Shoki Koyanagi, Yoshitaka Tanimura; The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach. J. Chem. Phys. 7 July 2022; 157 (1): 014104. https://doi.org/10.1063/5.0093666
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