Universal approach to quantum thermodynamics of strongly coupled systems under nonequilibrium conditions and external driving

Dou, Wenjie; Bätge, Jakob; Levy, Amikam; Thoss, Michael

doi:10.1103/physrevb.101.184304

Cited by 28 publications

(31 citation statements)

References 82 publications

(105 reference statements)

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“…Thus, a system-bath model, in which a small quantum system is coupled to a bath typically modeled by an infinite number of harmonic oscillators, has been employed to study open quantum dynamics. [11][12][13][14][15][16][17][18][19][20] This system-bath model can describe the time irreversibility of the dynamics as the system evolves toward thermal equilibrium in which the energy supplied by fluctuations and the energy lost through dissipation are balanced. The temperature of the bath does not change because its heat capacity is infinite.…”

Section: Introductionmentioning

confidence: 99%

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

Sakamoto

Tanimura

2020

The Journal of Chemical Physics

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We present a scheme to evaluate thermodynamic variables for a system coupled to a heat bath under a time-dependent external force using the quasi-static Helmholtz energy from the numerically "exact" hierarchical equations of motion (HEOM). We computed the entropy produced by a spin system strongly coupled to a non-Markovian heat bath for various temperatures. We showed that when changes to the external perturbation occurred sufficiently slowly, the system always reached thermal equilibrium. Thus, we calculated the Boltzmann entropy and the von Neumann entropy for an isothermal process, as well as various thermodynamic variables, such as changes in internal energies, heat, and work, for a system in quasi-static equilibrium based on the HEOM. We found that although the characteristic features of the system entropies in the Boltzmann and von Neumann cases as a function of the system-bath coupling strength are similar, those for the total entropy production are completely different. The total entropy production in the Boltzmann case is always positive, whereas that in the von Neumann case becomes negative if we chose a thermal equilibrium state of the total system (an unfactorized thermal equilibrium state) as the initial state. This is because the total entropy production in the von Neumann case does not properly take into account the contribution of the entropy from the system-bath interaction. Thus, the Boltzmann entropy must be used to investigate entropy production in the fully quantum regime. Finally, we examined the applicability of the Jarzynski equality.

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Section: Introductionmentioning

confidence: 99%

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

Sakamoto

Tanimura

2020

The Journal of Chemical Physics

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“…The thermal conduction mechanism could be integrated in the current thermomechanical method. There would be so many applications, for example, the irreversible processes such as friction, ignition, combustion and detonation mechanisms [30] [31] [32] [33] [34], mechanical heat engines, quantum heat engines [35] [36] [37] [38], solar-powered, high and low temperature differential Stirling engines [39] [40] [41], quantum thermodynamic systems [42] [43] [44]. The mechanism of drinking bird is more sophisticated and fundamental than that of Stirling engines, because it spontaneously converts thermal energy into mechanical energy and thermodynamic work by way of the concept of entropy-flow.…”

Section: T > τmentioning

confidence: 99%

Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

Uechi¹,

Uechi²,

Uechi³

2021

JAMP

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The irreversible mechanism of heat engines is studied in terms of thermodynamic consistency and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The couplings among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, ( ) ( ) d T t t  , internal energy, ( ) d t  , and thermodynamic work, ( )dW t , are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.

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“…( 4), ( 5) and ( 6)] we present a numerical example of a quantum Otto heat engine (see Fig. 1) that extracts work from heat baths with a resonant level model [44,45,47,48,[52][53][54][55][56][57],…”

mentioning

confidence: 99%

Periodically-driven quantum thermal machines from warming up to limit cycle

Liu,

Jung,

Segal

2021

Preprint

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Theoretical treatments of periodically-driven quantum thermal machines (PD-QTMs) are largely focused on the limit-cycle stage of operation characterized by a periodic state of the system. Yet, this regime is not immediately accessible for experimental verification. Here, we present a general thermodynamic framework that can handle the performance of PD-QTMs both before and during the limit-cycle stage of operation. It is achieved by observing that periodicity may break down at the ensemble average level, even in the limit-cycle phase. With this observation, and using conventional thermodynamic expressions for work and heat, we find that a complete description of the first law of thermodynamics for PD-QTMs requires a new contribution, which vanishes only in the limit-cycle phase under rather weak system-bath couplings. Significantly, this contribution is substantial at strong couplings even at limit cycle, thus largely affecting the behavior of the thermodynamic efficiency. We demonstrate our framework by simulating a quantum Otto engine building upon a driven resonant level model. Our results provide new insights towards a complete description of PD-QTMs, from turn-on to the limit-cycle stage and, particularly, shed light on the development of quantum thermodynamics at strong coupling.

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Universal approach to quantum thermodynamics of strongly coupled systems under nonequilibrium conditions and external driving

Cited by 28 publications

References 82 publications

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

Periodically-driven quantum thermal machines from warming up to limit cycle

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