Executive Summary : | The equilibrium statistical mechanics merges with the thermodynamics for quasistatic processes in a system's thermodynamic limit. The limit for reaching quantum thermodynamics from quantum nonequilibrium statistical mechanics has not been defined yet. However, it is possible to define such a limit for an open quantum system by describing it in terms of both quantum thermodynamics and quantum nonequilibrium statistical mechanics. An appropriate system for this would be a Bose or Fermi gas of oscillators with a time-dependent frequency. This would provide interesting research work on time-dependent finite-size effects on quantum mechanical systems at very low temperatures, such as micro Kelvin or less. Another interesting system could be a gas of 2-level atoms in a resonant optical cavity or an array of cavities, using models like Jaynes-Cummings or Tavis-Cummings. The physical and thermodynamic properties of ultracold systems of Bose and Fermi gases of alkali atoms are observed in magneto-optical traps, which are the size of micrometers. This makes mesoscopic physics, ultracold systems, quantum thermodynamics, and cavity quantum electrodynamics relevant in the current context. The main objective is to relate quantum nonequilibrium statistical mechanics and quantum thermodynamics at the mesoscopic length scale. The methodology for this project includes testing equations/models such as the schrodinger equation, Lindblad master equation, Jaynes-Cummings model, Tavis-Cummings model, Quantum Langevin equation, Fokker-Planck equation, Jarzinski equality, Boltzmann equation, Caldeira-Leggett model, and Floquet oscillation. |