  We show that an open fermionic system coupled to continuous environment with
unitary system-environment evolution can be exactly mapped onto an auxiliary
system consisting of the physical fermion system and a set of discrete
fermionic modes subject to non-unitary Lindblad-type system-modes evolution in
such a way that reduced dynamics of the fermionic system in the two cases are
the same. Conditions for equivalence of reduced dynamics in the two systems are
identified and a proof is presented. The study is extension of recent work on
Bose systems [D. Tamascelli, A. Smirne, S. F. Huelga, and M. B. Plenio, Phys.
Rev. Lett. 120, 030402 (2018)] to open quantum Fermi systems and to multi-time
correlation functions. Numerical simulations within generic junction model are
presented for illustration.
