  Topological phases of matter are protected from local perturbations and
therefore have been thought to be robust against decoherence. However, it has
not been systematically explored whether and how topological states are
dynamically robust against the environment-induced decoherence. In this Letter,
we develop a theory for topological systems that incorporate dissipations,
noises and thermal effects. We derive novelly the exact master equation and the
transient quantum transport for the study of dissipative topological systems,
mainly focusing on noninteracting topological insulators and topological
superconductors. The resulting exact master equation and the transient
transport current are also applicable for the systems initially entangled with
environments. We apply the theory to the topological Haldane model (Chern
insulator) and the quantized Majorana conductance to explore topological phases
of matter that incorporate dissipations, noises and thermal effects, and
demonstrate the dissipative dynamics of topological states.
