Nonlocal Work in Time-dependent Open Quantum Systems

How to rigorously define thermodynamic quantities such as heat, work, and internal energy in open quantum systems driven far from equilibrium by the action of time-dependent forces remains a significant open question in quantum thermodynamics. We shed light on this problem by elucidating the nonlocal character of the quantum work performed on such systems and show to what extent one can formulate the first law of thermodynamics for such systems in both the transient and the late-time regimes. The consistency of this scheme with the second and third laws of thermodynamics is also demonstrated. Importantly, it is shown how nonlocal work can be leveraged to obtain quantum advantage locally in a quantum lever or through quantum noise cancellation. We derive closed-form expressions for thermodynamic quantities using nonequilibrium Green's functions (NEGF) and illustrate the formal results by simulating the thermodynamics of a quenched resonant-level model coupled strongly to a reservoir. The formalism developed is then applied to analyze the thermodynamic performance of a model quantum machine: a driven two-level quantum system strongly coupled to two metallic reservoirs, which can operate in several configurations–as a chemical pump/engine or a heat pump/engine.