The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach

Abstract

Using the quasi-equilibrium Helmholtz energy (qHE), 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 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.

11 pages 2 figures. arXiv admin note: text overlap with arXiv:2205.09487

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Cited by in corpus (9)

• Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams
• Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle
• Pseudomode treatment of strong-coupling quantum thermodynamics
• Classical and quantum thermodynamics in a non-equilibrium regime: Application to Stirling engine
• Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle
• Multimode Brownian oscillators: Exact solutions to heat transport
• Input-Output Hierarchical Equations Of Motion