[AYBABTME]

If something is already bumping around randomly, all you need to do is constrain the bumping along some dimensions and it will move less randomly and more frequently toward the remaining free dimensions.

That's easier than having to provide all the energy to do the movement directly.

[quux]

Constrained energy basically acts as mass right? So would an intuitive way to think of this be that the warm particle has more energy, but moving it confines where that energy can be so it behaves as if it has more mass?