Conjecture: “A fast frictionless ball that recurrently passes through “grooves” with a lowered, locally time-periodic potential loses energy on average in forward time for non-selected initial conditions.”
Even a single such groove on a ring predictably suffices. This mechanical toy then qualifies as a prototype example for dynamical friction.
Corollary: If the vibrating grooves are replaced by vibrating mounds, the ball statistically gains energy in forward time for non-selected initial conditions.
Conclusion: These are the 2 deterministic prototypes of statistical dynamical behavior in the cosmos: cryodynamics and thermodynamics. Life is an implication of the latter. The former is still largely unexplored. I thank my Tübingen group for discussions.