[Cleonis]

Here is one way of looking at it: statistical mechanics introduced the concept of entropy.

Years ago, in school, the physics teacher gave the following vivid demonstration:

The demonstration involved two beakers, stacked, the openings facing each other, initially a sheet of thin cardboard separated the two.

In the bottom beaker a quantity of Nitrogen dioxide gas had been had been added. The brown color of the gas was clearly visible. The top beaker was filled with plain air, so it was colorless.

Nitrogen dioxide is denser than air. If the gases would not mix then all of the Nitrogen dioxide would stay in the bottom beaker. But of course the two do mix.

When the separator was removed we saw the brown color of the Nitrogen dioxide rise to the top. In less than half a minute the combined space was an even brown color.

And then the teacher explained the significance: in the process of filling the entire space the heavier Nitrogen dioxide molecules had displaced lighter molecules. That is: a significant part of the population of Nitrogen dioxide had moved against the pull of gravity. This move against gravity is probability driven.

Statistical mechanics provides the means to treat this process quantitatively. You quantify by counting numbers of states. Mixed states outnumber separated states - by far.

The climbing of the Nitrogen dioxide molecules goes at the expense of the temperature of the combined gases. That is, if you make sure that in the initial state the temperature in the two compartments is the same then you can compare the final temperature with that. The temperature of the final mixture will be a bit lower than the starting temperature. That is, some kinetic energy has been converted to gravitational potential energy.

So in this particular demonstration probability was acting in a direction opposite to gravity, and overall probability had the upper hand.

Probability effects fall in the category of emergent phenomena. An emergent phenomenon is somewhat of an in-between category. Not quite as fundamental as the law of gravity, but there is no denying that it has an existence of its own.