In relativity momentum is associated with flux of energy (not just mass), e.g. for a single particle $\textbf{p} = (E/c^2)\textbf{v}$
Imagine a rod which initially is hotter on one end. If the rod is thermally isolated, heat will start to propagate through the rod until the temperature equalizes.
Does this mean that rod will start moving in the direction of the hotter end to compensate for non-zero momentum associated with the heat flow? It should be moving until the heat flow stops and should preserve the center of energy point (not center of mass).
Are there any known physical effects that are related to this? It looks kinda cool. I realize that in the "real-world" it should be small, but maybe in high-energy or plasma physics..