On the First Law of Thermodynamics in Time-Dependent Open Quantum Systems

An unambiguous operator is established for the internal energy of an interacting time-dependent open quantum system, shedding light on a long-standing debate about how exactly the First Law of Thermodynamics should be formulated for such systems. We arrive at this using a key insight from Mesoscopics: infinitely far away from the local driving and coupling of an open quantum system, reservoirs are only infinitesimally perturbed from equilibrium, allowing one to unambiguously define Heat in strongly driven systems. Fully general expressions for the quantum-statistical averages of the heat current and the power delivered by various agents to the system are derived using Non-Equilibrium Green's Functions, establishing an experimentally meaningful and quantum mechanically consistent division of the energy of the system under consideration into Heat flowing from and Work done on the system. Motivated by previous work¹, we apply our formalism to analyze the thermodynamic performance of a model quantum machine: a pulsed 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.

¹C. A. Stafford and Ned S. Wingreen, Phys. Rev. Lett. 76, 1916 (1996).