  The adiabatic approximation exhibits wide applicability in quantum mechanics,
providing a simple approach for nontransitional dynamics in quantum systems
governed by slowly varying time-dependent Hamiltonians. However, the standard
adiabatic theorem is specifically derived for closed quantum systems. In a
realistic open system scenario, the inevitable system-reservoir interaction
must be taken into account, which strongly impacts the generalization of the
adiabatic behavior. In this paper, we introduce sufficient conditions for the
adiabatic approximation in open quantum systems. These conditions are simple
yet general, providing a suitable instrument to investigate adiabaticity for
arbitrary initial mixed states evolving under time local master equations. We
first illustrate our results by showing that the adiabatic approximation for
open systems is compatible with the description of quantum thermodynamics at
thermal equilibrium, where irreversible entropy production is vanishing. We
also apply our sufficient conditions as a tool in quantum control, evaluating
the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and
the Landau-Zener model under decoherence.
