  We propose a theory of adiabaticity in quantum Markovian dynamics based on a
decomposition of the Hilbert space induced by the asymptotic behavior of the
Lindblad semigroup. A central idea of our approach is that the natural
generalization of the concept of eigenspace of the Hamiltonian in the case of
Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor.
Unlike previous attempts to define adiabaticity for open systems, our approach
deals exclusively with physical entities and provides a simple, intuitive
picture at the underlying Hilbert-space level, linking the notion of
adiabaticity to the theory of noiseless subsystems. As an application of our
theory, we propose a framework for decoherence-assisted computation in
noiseless codes under general Markovian noise. We also formulate a
dissipation-driven approach to holonomic computation based on adiabatic
dragging of subsystems that is generally not achievable by non-dissipative
means.
