A thermodynamically consistent Markovian master equation beyond the secular approximation

Potts, Patrick P.; Kalaee, Alex Arash Sand; Wacker, Andreas

doi:10.1088/1367-2630/ac3b2f

Cited by 35 publications

(15 citation statements)

References 66 publications

(128 reference statements)

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“…We note that our treatment here is a specific implementation of a generic approach, presented in Ref. [62]. For a different approach to treating the term dropped in Eq.…”

Section: The Laws Of Thermodynamicsmentioning

confidence: 99%

Probabilistically violating the first law of thermodynamics in a quantum heat engine

2022

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Fluctuations of thermodynamic observables, such as heat and work, contain relevant information on the underlying physical process. These fluctuations are however not taken into account in the traditional laws of thermodynamics. While the second law is extended to fluctuating systems by the celebrated fluctuation theorems, the first law is generally believed to hold even in the presence of fluctuations. Here we show that in the presence of quantum fluctuations, also the first law of thermodynamics may break down. This happens because quantum mechanics imposes constraints on the knowledge of heat and work. To illustrate our results, we provide a detailed case-study of work and heat fluctuations in a quantum heat engine based on a circuit QED architecture. We find probabilistic violations of the first law and show that they are closely connected to quantum signatures related to negative quasi-probabilities. Our results imply that in the presence of quantum fluctuations, the first law of thermodynamics may not be applicable to individual experimental runs.

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“…We note that our treatment here is a specific implementation of a generic approach, presented in Ref. [62]. For a different approach to treating the term dropped in Eq.…”

Section: The Laws Of Thermodynamicsmentioning

confidence: 99%

Probabilistically violating the first law of thermodynamics in a quantum heat engine

2022

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“…One of the major tools for theoretical analysis of such systems is the master equation approach [17][18][19][20][21]. Despite the enormous progress, so far the approach has been fully established only in the framework of the Born-Markov approximation [5,6,18,19,[22][23][24][25]. To handle the non-Markovian regimes for fermionic carriers the stochastic Schrödinger equation approaches with the correlated noise [26][27][28][29] have been put forward.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovian master equation for quantum transport of fermionic carriers

Maksimov,

Aksenov,

Kolovsky

2023

J. Phys.: Condens. Matter

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We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix (SPDM) in a closed form in both Markov and Born approximations. In the Markov approximation the master equation is solved analytically, whereas in the Born approximation the problem is reduced to an algebraic equation for the SPDM in the Redfield form. The non-Markovian equation is shown to lead to resonant transport similar to Landauer’s conductance. It is shown that in the deep non-Markovian regime the transport current can be matched with that obtained by the non-equilibrium Green’s function method.

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“…The issue of their thermodynamic consistency has been raised early on, and has in general been tackled by assuming the validity of detailed balance conditions, which impose strict constraints on the generator of the QME and on the associated steady-state density matrix [1][2][3][4][5][6][7]. The rapid development of quantum and stochastic thermodynamics [8,9] in recent years has created a renewed interest in this topic [10][11][12]. In particular, many efforts have been devoted to identifying conditions under which QMEs satisfy quantum analogs of classical fluctuation theorems (FT) [13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic consistency of quantum master equations

Soret

Cavina²,

Esposito³

2022

Phys. Rev. A

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Starting from a microscopic system-baths description, we derive the general conditions for a time-local quantum master equation (QME) to satisfy the first and second laws of thermodynamics at the fluctuating level. Using counting statistics, we show that the fluctuating second law can be rephrased as a generalized quantum detailed balance condition (GQDB), i.e., a symmetry of the time-local generators which ensures the validity of the fluctuation theorem. When requiring in addition a strict system-bath energy conservation, the GQDB reduces to the usual notion of detailed balance which characterizes QMEs with Gibbsian steady states. However, if energy conservation is only required on average, QMEs with non-Gibbsian steady states can still maintain a certain level of thermodynamic consistency. Applying our theory to commonly used QMEs, we show that the Redfield equation breaks the GQDB, and that some recently derived approximation schemes based on the Redfield equation (which hold beyond the secular approximation and allow one to derive a QME of Lindblad form) satisfy the GQDB and the average first law. We find that performing the secular approximation is the only way to ensure the first and second laws at the fluctuating level.

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A thermodynamically consistent Markovian master equation beyond the secular approximation

Cited by 35 publications

References 66 publications

Probabilistically violating the first law of thermodynamics in a quantum heat engine

Probabilistically violating the first law of thermodynamics in a quantum heat engine

Non-Markovian master equation for quantum transport of fermionic carriers

Thermodynamic consistency of quantum master equations

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