  We investigate departures from the Hamiltonian dynamics such as the quantum
decoherence in a supersymmetric quantum system due to its interaction with the
environment. The effective description is given by the
Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. The prescription
for supersymmetrization of this equation is elaborated and pairs of related
isospectral quantum systems are built. We present some instructive examples of
such a construction.
