Open quantum system dynamics and the mean force Gibbs state

Abstract

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