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arXiv:2404.14081 · Physical Review A

Nonadiabatic evolution and thermodynamics for a boundary-driven system with a weak intrasubsystem interaction

C. Jiang, Lei Shao

Published Sep 24, 2024• 0 citations
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Abstract

We derive a time-dependent master equation for an externally driven system, where the subsystems weakly interact with each other and are locally connected to the thermal reservoirs. The nonadiabatic equation obtained here can be viewed as a generalization of the local master equation, which has already been extensively used in describing the dynamics of a boundary-driven system. In addition, we investigate the fundamental reason underlying the thermodynamic inconsistency generated by the local and nonadiabatic master equations. We also provide a criterion to assess the consistency of these two equations with the second law of thermodynamics. Finally, we numerically confirm our results by considering a toy model consisting of two qubits and two local heat baths.

DOI
10.1103/physreva.110.032219

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We derive a time-dependent master equation for an externally driven system, where the subsystems weakly interact with each other and are locally connected to the thermal reservoirs. The nonadiabatic equation obtained here can be viewed as a generalization of the local master equation, which has already been extensively used in describing the dynamics of a boundary-driven system. In addition, we investigate the fundamental reason underlying the thermodynamic inconsistency generated by the local and nonadiabatic master equations. We also provide a criterion to assess the consistency of these two equations with the second law of thermodynamics. Finally, we numerically confirm our results by considering a toy model consisting of two qubits and two local heat baths.
Master equations under appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach provides a more convenient description than the global approach. However, these local master equations are believed to generate inconsistencies with the laws of thermodynamics when intersubsystem interactions exist. Here we develop an alternative local master equation by virtue of similar approximations used in deriving the traditional Gorini-Kossakowski-Lindblad-Sudarshan master equation. In particular, we stick to using eigenstates of each subsystem to construct quantum jump operators, and the secular approximation is also employed to modify the intersubsystem interactions. Our results show that violations of thermodynamic laws will be avoided after correcting intersubsystem interactions. Finally, we study a two-qubit heat transfer model and this further shows the validity of our modified master equation.
We construct a quantum Markovian master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the master equation to be extended beyond the adiabatic limit. The nonadiabatic master equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the nonadiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic master equation.
We investigate the dynamic evolution and thermodynamic process of a driven quantum system immersed in a finite-temperature heat bath. A Born-Markovian quantum master equation is formally derived for the time-dependent system with discrete energy levels. This quantum master equation can be applied to situations with a broad range of driving speeds and bath temperatures and thus be used to study the finite-time quantum thermodynamics even when nonadiabatic transition and dissipation coexist. The dissipative Landau-Zener model is analyzed as an example. The population evolution and transition probability of the model reveal the importance of the competition between driving and dissipation beyond the adiabatic regime. Moreover, local maxima of irreversible entropy production occur at intermediate sweep velocity and finite temperature, which the low-dissipation model cannot describe.
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).
We investigate the dynamics of a qubit chain locally coupled to a thermal reservoir, modeled through repeated collisions with particles drawn from a heat bath. Under suitable conditions, the resulting Lindblad equation is thermodynamically consistent -- it drives the system toward thermal equilibrium -- while remaining local at short times. This framework reveals a crossover between the global Lindblad equation derived from the secular approximation in weak-coupling theory and the local dissipative models often employed in the literature, which generally fail to ensure thermodynamic consistency.
A system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. A new quantum master equation which improves shortcomings of the master equation known in the so-called local approach is derived. The usual quantum master equation describing the weak coupling of the system with reservoir requires the knowledge of eigenvalues and eigenvectors of the Hamiltonian of the system, so it often becomes impractical. By this reason, when the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. However, recently, it was reported that the local approach master equation leads to the violation of the second law of thermodynamics. We develop a systematic perturbation expansion to derive corrections to the local approach master equation. Using this improvement of the local approach, we derive an expression for the heat flux for a particular model and show that it does not violate the second law of thermodynamics.