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We present an approach based on a density matrix expansion to studythermodynamic properties of a quantum system strongly coupled to two or morebaths. For slow external driving of the system, we identify the adiabatic andnonadiabatic contributions to thermodynamic quantities, and we show how thefirst and second laws of thermodynamics are manifested in the strong couplingregime. Particularly, we show that the entropy production is positive up tosecond order in the driving speed. The formulation can be applied both forBosonic and Fermionic systems, and recovers previous results for theequilibrium case (Phys. Rev. B 98, 134306 [2018]). The approach is thendemonstrated for the driven resonant level model as well as the driven Andersonimpurity model, where the hierarchical quantum master equation method is usedto accurately simulate the nonequilibrium quantum dynamics.

Universal approach to quantum thermodynamics of strongly coupled systems under nonequilibrium conditions and external driving