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Most non-equilibrium statistical processes of open time dependent systems are approached by Markovian dynamics of a system where time dependence of the system is assumed to be adiabatic (if Floquet theory is not possible due to the lack of periodicity). For open systems usually the Lindblad, Redfield or similar formalism are used in order to describe the time evolution of the density matrix.

What are the possible approaches and formalism one could use in order to describe the time evolution of the density matrix for an open system, where the time dependent processes happen on a non-adiabatic time scale? The aim would be to study dissipation and related phenomena for such a system.

This is a new field for me and I would be very grateful for some suggested starting points, advice and literature for my study of this topic.

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