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It is already known that the auxiliary density operators (ADOs) in the hierarchical equations of motion (HEOM) method contain system-bath interactions that are important in calculating various dynamical properties.This work extends a previous study (J.Chem.Phys.,130 164518 (2009)) in investigating the physical meaning of ADOs to lower temperature cases,where the non-Gaussian-Markovian terms can not be neglected.Here we derive exact relations between the expectation values of the collective bath coordinate and the ADOs.