  Recent works have shown that generic local Hamiltonians can be efficiently
inferred from local measurements performed on their eigenstates or thermal
states. Realistic quantum systems are often affected by dissipation and
decoherence due to coupling to an external environment. This raises the
question whether the steady states of such open quantum systems contain
sufficient information allowing for full and efficient reconstruction of the
system's dynamics. We find that such a reconstruction is possible for generic
local Markovian dynamics. We propose a recovery method that uses only local
measurements; for systems with finite-range interactions, the method recovers
the Lindbladian acting on each spatial domain using only observables within
that domain. We numerically study the accuracy of the reconstruction as a
function of the number of measurements, type of open-system dynamics and system
size. Interestingly, we show that couplings to external environments can in
fact facilitate the reconstruction of Hamiltonians composed of commuting terms.
