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arXiv:2204.09494 · Journal of Physics Condensed Matter

Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: non-equilibrium entropy production and higher order corrections

Kaiyi Tong, Wenjie Dou

Published Oct 12, 2022• 2 citations
arXivHTMLPDF

Abstract

Abstract We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Dou et al 2020 Phys. Rev. B 101 184304), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population, which is not determined previously in Dou et al (2020 Phys. Rev. B 101 184304). In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation.

DOI
10.1088/1361-648x/ac99c8

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Abstract We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Dou et al 2020 Phys. Rev. B 101 184304), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population, which is not determined previously in Dou et al (2020 Phys. Rev. B 101 184304). In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation.
We present an approach based on a density matrix expansion to study thermodynamic properties of a quantum system strongly coupled to two or more baths. For slow external driving of the system, we identify the adiabatic and nonadiabatic contributions to thermodynamic quantities, and we show how the first and second laws of thermodynamics are manifested in the strong coupling regime. Particularly, we show that the entropy production is positive up to second order in the driving speed. The formulation can be applied both for bosonic and fermionic systems, and recovers previous results for the equilibrium case [Phys. Rev. B 98, 134306 (2018)]. The approach is then demonstrated for the driven resonant level model as well as the driven Anderson impurity model, where the hierarchical quantum master equation method is used to accurately simulate the nonequilibrium quantum dynamics.
We study nonequilibrium thermodynamics in a fermionic resonant-level model with arbitrary coupling strength to a fermionic bath, taking the wide-band limit. In contrast to previous theories, we consider a system where both the level energy and the coupling strength depend explicitly on time. We find that, even in this generalized model, consistent thermodynamic laws can be obtained, up to the second order in the drive speed, by splitting the coupling energy symmetrically between system and bath. We define observables for the system energy, work, heat, and entropy, and calculate them using nonequilibrium Green's functions. We find that the observables fulfill the laws of thermodynamics, and connect smoothly to the known equilibrium results.
We present a consistent thermodynamic theory for the resonant level model in the wide-band limit, whose level energy is driven slowly by an external force. The problem of defining ``system'' and ``bath'' in the strong-coupling regime is circumvented by considering as the system everything that is influenced by the externally driven level. The thermodynamic functions that are obtained to first order beyond the quasistatic limit fulfill the first and second law with a positive entropy production, successfully connect to the forces experienced by the external driving, and reproduce the correct weak-coupling limit of stochastic thermodynamics.
Abstract The entropy produced when a quantum system at thermal equilibrium is driven to a non-equilibrium state can be considered as having components from coherence generation and from a population mismatch. The entropy component which is related to coherence represents a truly quantum effect and can be calculated using two different decompositions, based on either the relative entropy of coherence or on the thermal state corresponding to the Hamiltonian dephased in the eigen basis of the actual state. However, the decomposition based on the relative entropy was unable to quantify highly coherent processes or processes occurring in the low temperature regime. We experimentally explored a general driving scheme (a non-equilibrium process) on a nuclear magnetic resonance quantum processor, and were able to isolate the contribution of coherence to irreversible entropy generation. Furthermore, we numerically explored an infinitesimal driving process to distinguish between high and low temperature limits. The thermal equilibrium temperature and the final energy gap were varied to establish the relationship among temperature, energy level spacing, entropy production and coherence generation. Our results indicate that the contribution to entropy from coherence is higher in the low temperature regime. We also verified a generalized Clausius inequality, which affirms that the irreversible entropy production is lower-bounded.
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 present a protocol for the study of the dynamics and thermodynamics of quantum systems strongly coupled to a bath and subject to an external modulation. Our protocol quantifies the evolution of the system-bath composite by expanding the full density matrix as a series in the powers of the modulation rate, from which the functional form of work, heat, and entropy rates can be obtained. Under slow driving, thermodynamic laws are established. The entropy production rate is positive and is found to be related to the excess work dissipated by friction, at least up to second order in the driving speed. As an example of the present methodology, we reproduce the results for the quantum thermodynamics of the driven resonance level model. We also emphasize that our formalism is quite general and allows for electron-electron interactions, which can give rise to exotic Kondo resonances appearing in thermodynamic quantities.