Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

Strasberg, Philipp; Schaller, Gernot; Lambert, Neill; Brandes, Tobias

doi:10.1088/1367-2630/18/7/073007

Cited by 201 publications

(248 citation statements)

References 89 publications

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“…The access afforded by the RC formalism to hitherto unexplored regimes are compelling reasons to apply the techniques discussed here to such models, as in Ref. [41].…”

Section: Discussionmentioning

confidence: 99%

Performance of a quantum heat engine at strong reservoir coupling

2017

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We study a quantum heat engine at strong coupling between the system and the thermal reservoirs. Exploiting a collective coordinate mapping, we incorporate system-reservoir correlations into a consistent thermodynamic analysis, thus circumventing the usual restriction to weak coupling and vanishing correlations. We apply our formalism to the example of a quantum Otto cycle, demonstrating that the performance of the engine is diminished in the strong coupling regime with respect to its weakly coupled counterpart, producing a reduced net work output and operating at a lower energy conversion efficiency. We identify costs imposed by sudden decoupling of the system and reservoirs around the cycle as being primarily responsible for the diminished performance, and define an alternative operational procedure which can partially recover the work output and efficiency. More generally, the collective coordinate mapping holds considerable promise for wider studies of thermodynamic systems beyond weak reservoir coupling.

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“…The access afforded by the RC formalism to hitherto unexplored regimes are compelling reasons to apply the techniques discussed here to such models, as in Ref. [41].…”

Section: Discussionmentioning

confidence: 99%

Performance of a quantum heat engine at strong reservoir coupling

2017

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“…(15) Similarly, the quantity h S ≡ u S þ ϕ, which is often called the Hamiltonian of mean force [14][15][16][17][33][34][35][36], obeys…”

Section: B Solvated Ensemblementioning

confidence: 99%

“…In some situations involving quantum systems, one can choose a reaction coordinate that effectively transforms a strongly coupled system to a weakly coupled one [36]. Other cases are usefully studied using a nonequilibrium Green's function approach [80,81] or a path integral approach [82].…”

Section: Present Workmentioning

confidence: 99%

Stochastic and Macroscopic Thermodynamics of Strongly Coupled Systems

2017

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We develop a thermodynamic framework that describes a classical system of interest S that is strongly coupled to its thermal environment E. Within this framework, seven key thermodynamic quantitiesinternal energy, entropy, volume, enthalpy, Gibbs free energy, heat, and work-are defined microscopically. These quantities obey thermodynamic relations including both the first and second law, and they satisfy nonequilibrium fluctuation theorems. We additionally impose a macroscopic consistency condition: When S is large, the quantities defined within our framework scale up to their macroscopic counterparts. By satisfying this condition, we demonstrate that a unifying framework can be developed, which encompasses both stochastic thermodynamics at one end, and macroscopic thermodynamics at the other. A central element in our approach is a thermodynamic definition of the volume of the system of interest, which converges to the usual geometric definition when S is large. We also sketch an alternative framework that satisfies the same consistency conditions. The dynamics of the system and environment are modeled using Hamilton's equations in the full phase space.

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“…Due to the weak coupling between supersystem and reservoirs, we identify the change in energy of the reservoir, calculated using the counting field χ ν , with the heat flow Q ṅ [37], defined to be positive if it flows into the system. For the hot bath and cold bath we define, respectively,…”

Section: Steady State Thermodynamicsmentioning

confidence: 99%

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

et al. 2018

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We combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born-Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and their efficiency and coefficient of performance decrease. Furthermore, our model can reproduce the setup of laser cooling of trapped ions in a specific parameter limit. [35,36], redefined system-reservoir partitions (collective coordinate (CC) mappings) [37-41], a quantum absorption refrigerator [42], quenched thermodynamic protocols [43,44] and the derivation of an exact expression for the entropy production of a finite arbitrary system in contact with one or several thermal reservoirs [45], but none of which were applied to periodically driven machines so far. Exceptions are [46] and [47]. In [46] a polaron transformation and Floquet theory were used to include arbitrary strong coupling effects but only as long as the rotating wave approximation for the system Hamiltonian and the Markovian approximation for the reservoir hold. In [47] a periodically driven three-level heat engine was studied using the numerical method of hierarchy of equations of motion, an approach that is based in a decomposition of the bath correlation function rather than an explicit representation of the bath. For this reason, access to more general, thermodynamically relevant thermal transport properties requires a tailored solution [48].However, none of the aforementioned methods was successfully applied to the combinations of problems we want to tackle: a driven system coupled to multiple heat reservoirs with a possibly strong, driven and non-Markovian coupling. To achieve this we combine three methods: a CC mapping [49,50], Floquet theory for open systems [14,21] and full counting statistics [51]. This novel and unique combination provides access to steady state thermodynamics lifting the restriction of common assumptions such as a very fast driving, Markovian and weakly coupled reservoirs, and the secular approximation. First, in the CC mapping, we identify a collective degree of freedom in the reservoir, sometimes referred to as reaction coordinate [52] that is responsible for the strong coupling and non-Markovian effects. Second, using Floquet theory, we derive a master equation for the original system plus CC and apply full counting statistics methods to obtain the change in energy of the reservoirs unambiguously. This strategy allows us to perform a consistent thermodynamic analysis of periodically driven thermal machines. Furthermore, it also allows us to accurately treat periodic time dependencies in the interaction between system and res...

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Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

Cited by 201 publications

References 89 publications

Performance of a quantum heat engine at strong reservoir coupling

Performance of a quantum heat engine at strong reservoir coupling

Stochastic and Macroscopic Thermodynamics of Strongly Coupled Systems

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

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