I recently got into a discussion whether and how the Coriolis force/effect is related to gravitation.

Is gravitation involved in the Coriolis force? If so, how could that be explained?

This is a physical rather than a mathematical justification - ignore my answer if that isn't what you wanted!

All systems have some thermal motion so they explore the phase space in their immediate vicinity. If there is a nearby point with a free energy lower by some amount $\Delta G$ then the relative probability of finding the system at that point will be $\exp(-\Delta G/RT)$. So if the energy is minimised by moving to that point, i.e.$\Delta G < 0$, we just have to wait and we'll find the system has moved there. The only place in phase space the system won't move is when the free energy is at a (local) minimum. That's why a system always (locally) minimises its free energy if you wait long enough.
