Nonadiabatic evolution and thermodynamics of a time-dependent open quantum system

We investigate the dynamic evolution and thermodynamic process of a driven quantum system immersed in finite-temperature heat bath. A Born-Markovian master equation is formally derived for time-dependent with discrete energy levels. This can be applied to situations broad range driving speeds bath temperatures thus used study finite-time thermodynamics even when nonadiabatic transition dissipation coexist. The dissipative Landau-Zener model analyzed as an example. population probability reveal importance competition between beyond adiabatic regime. Moreover, local maximums irreversible entropy production occur at intermediate sweep velocity finite temperature, which low-dissipation cannot describe.