Open quantum system dynamics and the mean force Gibbs state

The dynamical convergence of a system to the thermal distribution, or Gibbs state, is standard assumption across all physical sciences. state determined just by temperature and system's energies alone. But at decreasing sizes, i.e. for nanoscale quantum systems, interaction with their environments not negligible. question then arises: Is steady still state? And if not, how may depend on details? Here we provide an overview recent progress answering these questions. We expand state-of-the-art along two general avenues: First take static point-of-view which postulates so-called mean force state. This view commonly adopted in field strong coupling thermodynamics, where modified laws thermodynamics non-equilibrium fluctuation relations are established basis this Second, point-of-view, originating from open examines time-asymptotic within paradigms. describe mathematical paradigm proves return equilibrium, discuss number microscopic methods, particularly master equations. conclude summary links between statics equilibration dynamics, extensive list problems. comprehensive will be interest researchers wider fields mesoscopic physics, statistical physics optics, find applications whenever energy exchanged nanoscale, chemistry biology, magnetism heat management.