Computation of transient dynamics of energy power for a dissipative two state system

We consider a two-level system coupled to a thermal bath and we investigate the variation of energy transferred to the reservoir as a function of time. The physical quantity under investigation is the time-dependent quantum average power. We compare quantum master equation approaches with the functional influence method. Differences and similarities between the methods are analysed, showing deviations at low temperature between the functional integral approach and the predictions based on master equations.