True, though I don't believe there is any reason to think such systems would actually be physically realizable. To me this seems similar to the dome shape where

True, though I don't believe there is any reason to think such systems would actually be physically realizable. To me this seems similar to the dome shape where a ball sitting at rest on the top would randomly move down at any time in any direction - it is part of the mathematics of Newtonian mechanics, but it is not necessarily part of the physics of it (since that dome shape requires infinite smoothness, which can't exist in the physical model).