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The uniqueness issue of SDE decomposition theory proposed by Ao and hisco-workers has recently been discussed. A comprehensive study to investigateconnections among different landscape theories [J. Chem. Phys. 144, 094109(2016)] has pointed out that the decomposition is generally not unique, whileAo et al. (arXiv:1603.07927v1) argues that such conclusions are "incorrect"because of the missing boundary conditions. In this comment, we will combineliteratures research and concrete examples to show that the concrete andeffective boundary conditions have not been proposed to guarantee theuniqueness, hence the arguments in [arXiv:1603.07927v1] are not sufficient.Moreover, we show that the "uniqueness" of the O-U process decompositionreferred by YTA paper is unable to serve as a counterexample to ZL's resultsince additional assumptions have been made implicitly beyond the original SDEdecomposition framework, which cannot be applied to general nonlinear cases.Some other issues such as the failure of gradient expansion method will also bediscussed. Our demonstration contributes to better understanding of therelevant papers as well as the SDE decomposition theory.

Comment on "On Uniqueness of SDE Decomposition in A-type Stochastic Integration" [arXiv:1603.07927v1]