[posterboy]

The common depiction is of a bunch of particles of two kinds, sorted into separate compartments by kind, which will mix if a divider is removed. In this picture, every part of one kind receiving a partner of the other kind, that can be called a state of order. If we take heat instead, every particle swinging differently is more chaotic--at least in my understanding--than all synching up so that their speeds relative to each other are zero ... 0 degree is just not higher order, because "high" is associated with high frequency (or energy or order).

In your shaky example, you transmit energy to the system by shaking, so if shaking a certain way, you'd well expect standing waves, if shaking a bit more you'd pulverize the marble and ultimately a hot plasma with density gradients. I wonder how hard you'd have to shake and swirl to eventually get a black hole, for which the notion of entropy doesn't even really make sense, if you aren't inside.