  The interplay between the non-Hermitian skin effect and the imaginary gap of
lossy lattices results in the edge burst, a boundary-induced dynamical
phenomenon in which an exceptionally large portion of particle loss occurs at
the edge. Here, we find that this intriguing non-Hermitian dynamical phenomenon
can be exactly mapped into the steady-state density distribution of a
corresponding open quantum system. Consequently, the bulk-edge scaling relation
of loss probability in the edge burst maps to that of steady-state density.
Furthermore, we introduce a many-body open-system model in which the two-body
loss generates an interaction-induced non-Hermitian skin effect. Using the
positive-$P$ method, we demonstrate the validity of the scaling relation for
steady-state correlators. These results provide a unique perspective on the
interaction-induced many-body non-Hermitian skin effect. Our predictions are
testable in state-of-the-art experimental platforms.
