The arrow of what now?[1] This is classical dynamics we're doing.
I repeat, this is a math result, not an argument about physical systems.
[1] Edit as this was clearly missed: THIS IS SARCASM. Thermodynamics and statistical mechanics are excellent theories and worth studying as they tell us deep and profound things about the natural world. This particular novelty is a result from classical dynamics where they don't apply. The "arrow of time" in Newtonian mechanics is absolutely reversible, and there is no Newtonian idea of "entropy".
did you? the title and content of this post is about math results. you should really consider the possibility that you're very wrong here.
the discussion is about hypothetical results from classical mechanics, which, along with the rest of physics, is a mathematical model that may be incongruous with observations.
I suggest you read the HN guidelines, you are quite abrasive and aggressive in your posts.
Regarding your post about entropy. The reason it does not apply is because entropy is a concept from statistical mechanics which is about the statistics of ensembles of many (even non-classical) particles. It's a concept invented after Newton dynamics, but does not apply to describing the equations of motion of a single particle (try to define the entropy of the single particle system). Time reversal is a core tenent of Newton dynamics.
Maybe you should read my most, I didn't say that statistical mechanics is nonclassical. I said statistical mechanics does not apply to the discussion of a single particle rolling up or down a slope. Tell me which of the states has more entropy the one with the particle at the top od the Norton dome or the one at the bottom?
The arrow of what now?[1] This is classical dynamics we're doing.
I repeat, this is a math result, not an argument about physical systems.
[1] Edit as this was clearly missed: THIS IS SARCASM. Thermodynamics and statistical mechanics are excellent theories and worth studying as they tell us deep and profound things about the natural world. This particular novelty is a result from classical dynamics where they don't apply. The "arrow of time" in Newtonian mechanics is absolutely reversible, and there is no Newtonian idea of "entropy".