Local knowledge

Consider a local element in an aggregation with no global knowledge which moves toward minimum density.   It has no uniform knowledge of any dx, and can only make globally stable movements if all elements were of standard size and queued up fairly.  Normally elements avoid queueing and that makes spheres happen as queuing decreases toward the perimeter.

It is not sufficient for all elements to be the same size, they also need to have the same time constant in their movements. Otherwise unnecessary movements starts, and that is not maximum entropy. So element size and time constant have to be equalized.

Now, what happens if there is no optimum move? The element still needs to maintain time constant and will make a random move, I would think. The element itself must always have a self induced imbalance so that its current position in not optimum.

Do these exchanging elements  pack spheres better than the inerts? I would think so, I would think that aggregating empty positions allows more packing by movement, though I cannot prove this. If I had to prove this I would look at a perturbed system, one not in equilibrium. Then, stable configurations must come and go  as it moves toward equilibrium.

If movements are quantized, then is their a background grid system?  Not if the elements are making moves in the second differential and are perturbed.  So empty space is sub optimal, entropy is not always increasing in a static discrete space.

The last point is why any system needs inert nulls plus one active element.  How many other elements does the system need? As many as needed to work the differential order.  If the perturbations are not linear, then a single active element results in repeated movements, entropy is not increasing.