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.
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