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)2469-995010.1103/PhysRevB.98.134306]. 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.
Bibliographical noteFunding Information:
This work was supported by the Department of Energy, Photonics at Thermodynamic Limits Energy Frontier Research Center, under Grant No. DE-SC0019140 and a research grant of the German Research Foundation (DFG). Furthermore, support by the state of Baden-Württemberg through bwHPC and the DFG through Grant No. INST 40/467-1 FUGG is gratefully acknowledged. M.T. thanks Eran Rabani for many insightful discussion on nonequilibrium quantum transport and for kindly hosting his sabbatical stay at the Chemistry Department of the University of California at Berkeley.
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