Open Quantum Dynamics Theory for Non-Equilibrium Work: Hierarchical Equations of Motion Approach

Sakamoto, Souichi; Tanimura, Yoshitaka

doi:10.7566/jpsj.90.033001

Cited by 14 publications

(18 citation statements)

References 36 publications

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“…The distinctive feature of the HEOM approach is that it can rigorously evaluate changes in heat and entropy not only for the system but also for the bath and the SB interaction (117). We thus showed that quantum thermodynamics can be described in the framework of statistical mechanics, even in the nonequilibrium case, by regarding nonequilibrium work as a change in quasi-static free energy (131,133).…”

Section: Quantum Statistical Thermodynamicsmentioning

confidence: 93%

Autobiography of Yoshitaka Tanimura

Tanimura

2021

J. Phys. Chem. B

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Section: Quantum Statistical Thermodynamicsmentioning

confidence: 93%

Autobiography of Yoshitaka Tanimura

Tanimura

2021

J. Phys. Chem. B

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“…The work under the quasi-static perturbations is regarded as thermodynamic work. 71,77 The quasiequilibrium Helmholtz energy (qHE) for the inverse bath temperature β is then introduced as ∆F qst α (β; t) = W qst α (β; t) for α = A, I 1 , and I 2 , where W qst α (β; t) is defined by Eqs. ( 16) and ( 17) using the quasi-static solution of the HEOM, which is expressed as ρqst n (t).…”

Section: Non-equilibrium Free Energymentioning

confidence: 99%

“…In the present paper, to clarify the relationship between quantum mechanics and statistical thermodynamics, we conduct quantum simulations of a Carnot cycle on the basis of an SB model from a quasi-static state to highly non-equilibrium states, for which the applicability of thermodynamic descriptions is not clear. Although such investigations have been conducted in a framework of open quantum dynamics theories, even in strong SB coupling cases (for example, for heat transport, [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] heat engines and refrigerators, entropy production, [69][70][71] non-equilibrium works, 18,72 and quantum information problems, 73,74 in addition to being applied as a context for the Jarzynski equality, [75][76][77] fluctuation theorems, [78][79][80][81][82][83] and Maxwell's demon [84][85][86] ), fully quantum investigations face difficulties because of the lack of a consistent thermodynamic formulation for a thermal system described by a Hamiltonian with external time-dependent perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, it was shown that the heat can be defined as the change in heat-bath energy 45,52 and the "quasi-static" free energy can be defined as the nonequilibrium work. 71,77 The behavior described with this open quantum dynamics approach has been examined using numerically "exact" hierarchical equations of motion (HEOM) 31,[87][88][89][90][91][92] and was found to be consistent with the first and second laws of thermodynamics for a quasi-static process. 93 This provides an ideal platform for examining fundamental propositions of quantum thermodynamics in the fully quantum regime.…”

Section: Introductionmentioning

confidence: 99%

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Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams

Koyanagi¹,

Tanimura²

2022

Preprint

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We conduct numerical simulations of a quantum Carnot cycle using the hierarchical equations of motion from quasi-static to highly non-equilibrium conditions. The Carnot engine is modeled by a two-level system coupled to hot and cold heat baths, and it is controlled by time-dependent external fields for the system and system-bath interactions. The field for the system controls isothermal processes (the isothermal driving field), whereas that for the system-bath interactions controls the transition between the isothermal and adiabatic processes (the adiabatic transition field). By regarding work as non-equilibrium free energy, we compute non-equilibrium thermodynamic variables, such as the magnetization and strain, for external perturbations. These are not state variables beside quasi-static case, but we introduce them in an attempt to characterize the thermal properties of the cycle. We then analyze the simulation results using thermodynamic work diagrams depicted as functions of these variables for various values of the system-bath coupling strength and the period of the Carnot cycle. It is shown that the efficiency of the Carnot cycle exhibits a maximum in the quasi-static limit of the modulation. We also find that the efficiency changes as a function of the system-bath coupling strength and reaches its maximum in the intermediate coupling-strength regime.

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“…[2][3][4][5][6] The heat bath is considered to be an unlimited heat source with infinite heat capacity. 7,8 However, the thermal noise from complex or frustrated materials is typically non-Gaussian, and its temporal and spatial correlations are non-uniform, although the ensemble average of the noise has a Gaussian profile when the strength of each source of noise is comparable, due to the central limit theorem. 9 The noise correlation is characterized by a simple function, for example, a stretched exponential function.…”

Section: Introductionmentioning

confidence: 99%

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

Nakamura,

Tanimura

2021

Preprint

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Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature, even when the anisotropy of the XXZ model is enormous. We also found that the population relaxation dynamics of the TLS changed in a complex manner with the change of the anisotropy and the ferromagnetic or antiferromagnetic orders of the spins.

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Open Quantum Dynamics Theory for Non-Equilibrium Work: Hierarchical Equations of Motion Approach

Cited by 14 publications

References 36 publications

Autobiography of Yoshitaka Tanimura

Autobiography of Yoshitaka Tanimura

Numerically "exact" simulations of a quantum Carnot cycle: Analysis using thermodynamic work diagrams

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

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