The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry

We present a canonical derivation of an influence superoperator which generates the reduced dynamics of a Fermionic quantum system linearly coupled to a Fermionic environment initially at thermal equilibrium. We use this formalism to derive a generalized-Lindblad master equation (in the Markovian limit) and a generalized version of the hierarchical equations of motion valid in arbitrary parity-symmetry conditions, important for the correct evaluation of system correlation functions and spectra.