  The paper concerns spontaneous asymptotic phase-locking and synchronization
in two-qubit systems undergoing continuous Markovian evolution described by
Lindbladian dynamics with normal Lindblad operators. Using analytic methods,
all phase-locking-enforcing mechanisms within the given framework are obtained
and classified. Detailed structures of their respective attractor spaces are
provided and used to explore their properties from various perspectives. Amid
phase-locking processes those additionally enforcing identical stationary parts
of both qubits are identified, including as a special case the strictest form
of synchronization conceivable. A prominent basis is presented which reveals
that from a physical point of view two main types of phase-locking mechanisms
exist. The ability to preserve information about the initial state is explored
and an upper bound on the amplitude of oscillations of the resulting
phase-locked dynamics is established. Permutation symmetry of both asymptotic
states and phase-locking mechanisms is discussed. Lastly, the possibility of
entanglement production playing the role of a phase-locking witness is rebutted
by three analytically treatable examples.
