  The extraordinary quantum properties of nonequilibrium systems governed by
dissipative dynamics have become a focal point in contemporary scientific
inquiry. The Nonequilibrium Green's Functions (NEGF) theory provides a
versatile method for addressing driven {\em non-dissipative} systems, utilizing
the powerful diagrammatic technique to incorporate correlation effects. We here
present a second-quantization approach to the {\em dissipative} NEGF theory,
reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending
the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation
theory for many-body Lindblad operators, the formalism enables correlated and
dissipative real-time simulations for the exploration of transient and
steady-state changes in the electronic, transport, and optical properties of
materials.
