Response to “Comment on ‘Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond”’ [J. Chem. Phys. 145, 147104 (2016)]

The uniqueness issue of SDE decomposition theory proposed by Ao and his co-workers has recently been discussed. A comprehensive study to investigate connections among different landscape theories [J. Chem. Phys. 144, 094109 (2016)] has pointed out that the decomposition is generally not unique, while Ao et al. recently argue that such conclusions are “incorrect” because the uniqueness of the decomposition for Ornstein-Uhlenbeck (O-U) process has been claimed before. In this response, we will demonstrate that the claimed “uniqueness” of the O-U process decomposition is invalid to serve as a counterexample according to the original definition of SDE decomposition. The absence of effective and concrete boundary conditions in previous SDE decomposition papers will be pointed out, and some other issues in the comment will also be responded.