  The Lieb-Robinson bound shows the existence of a maximum speed of signal
propagation in discrete quantum mechanical systems with local interactions.
This generalizes the concept of relativistic causality beyond field theory, and
provides a powerful tool in theoretical condensed matter physics and quantum
information science. Here, we extend the scope of this seminal result by
considering general Markovian quantum evolution, where we prove that an
equivalent bound holds. In addition, we use the generalized bound to
demonstrate that correlations in the stationary state of a Markov process decay
on a length-scale set by the Lieb-Robinson velocity and the system's relaxation
time.
