Energy minimization is a consequence of entropy maximization, as I derive here.

Broadly, when things fall into a lower energy minimum, they heat the rest of the Universe, which increases its entropy. Nature loves this.

> What decides which thing gets to have low energy?

The configuration with higher entropy. It has more ways to appear, so we see it more often. That’s the Second Law, in essence.

At equilibrium, there’s no difference in any intensive parameter: temperature, pressure, stress, chemical potential, surface tension, electric field, you name it.