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

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.