On the First Law of Thermodynamics in TimeDependent Open Quantum Systems
Abstract
How to rigorously define thermodynamic quantities such as heat, work, and internal energy in open quantum systems driven far from equilibrium remains a significant open question in quantum thermodynamics. Heat is a quantity whose fundamental definition applies only to processes in systems infinitesimally perturbed from equilibrium, and as such, must be accounted for carefully in stronglydriven systems. In this work, an unambiguous operator for the internal energy of an interacting timedependent open quantum system is derived using a key insight from Mesoscopics: infinitely far from the local driving and coupling of an open quantum system, reservoirs are indeed only infinitesimally perturbed. Fully general expressions for the heat current and the power delivered by various agents to the system are derived using the formalism of nonequilibrium Green's functions, establishing an experimentally meaningful and quantum mechanically consistent division of the energy of the system under consideration into Heat flowing out of and Work done on the system. The spatiotemporal distribution of internal energy in a stronglydriven open quantum system is also analyzed. This formalism is applied to analyze the thermodynamic performance of a model quantum machine: a driven twolevel quantum system strongly coupled to two metallic reservoirs, which can operate in several configurationsas a chemical pump/engine or a heat pump/engine.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 arXiv:
 arXiv:2208.06544
 Bibcode:
 2022arXiv220806544K
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 19 pages, 7 figures