R. P. Feynman and F. L. Vernon, Jr., Ann. Phys. (N.Y.) 24, 118 (1963).
 Jinshuang Jin, Xiao Zheng, and YiJing Yan, J. Chem. Phys. 128, 234703 (2008).
 Bj = −i Pν ´tt0 dτ Cμσν (t, τ )aνσ[ψ(τ )] + i Pν ´tt0 dτ Cμσ¯ν∗(t, τ )aνσ[ψ′(τ )]. B˜j is similar to Bj but with Cμσν/Cμσ¯ν∗ replaced by C˙ μσν /C˙ μσ¯ν∗.
 The validity of Dyson's equation in HEOM space is natural. One can directly verify Eq.(16) by inserting it into Eq.(5) and letting Lsf (t) = Lpr(t).
 In our theory, the fluctuation-dissipation theorem is naturally established. See Eq.(29).