  We introduce an alternative way to derive the generalized form of the master
equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105,
030401 (2010)] for an adiabatically steered two-level quantum system
interacting with a Markovian environment. The original derivation employed the
effective Hamiltonian in the adiabatic basis with the standard interaction
picture approach but without the usual secular approximation. Our approach is
based on utilizing a master equation for a non-steered system in the first
super-adiabatic basis. It is potentially efficient in obtaining higher-order
equations. Furthermore, we show how to select the phases of the adiabatic
eigenstates to minimize the local adiabatic parameter and how this selection
leads to states which are invariant under a local gauge change. We also discuss
the effects of the adiabatic noncyclic geometric phase on the master equation.
