  For sufficiently low reservoir temperatures, it is known that open quantum
systems subject to decoherent interactions with the reservoir relax towards
their ground state in the weak coupling limit. Within the framework of quantum
master equations, this is formalized by the Born-Markov-secular (BMS)
approximation, where one obtains the system Gibbs state with the reservoir
temperature as a stationary state. When the solution to some problem is encoded
in the (isolated) ground state of a system Hamiltonian, decoherence can
therefore be exploited for computation. The computational complexity is then
given by the scaling of the relaxation time with the system size $n$.
  We study the relaxation behavior for local and non-local Hamiltonians that
are coupled dissipatively with local and non-local operators to a bosonic bath
in thermal equilibrium. We find that relaxation is generally more efficient
when coherences of the density matrix in the system energy eigenbasis are taken
into account. In addition, the relaxation speed strongly depends on the matrix
elements of the coupling operators between initial state and ground state.
  We show that Dicke superradiance is a special case of our relaxation models
and can thus be understood as a coherence-assisted relaxation speedup.
