I understand that the increment/maximization of Entropy (of the universe) is "Accompanied" with all "Natural" phenomena we see. In many of the questions, I and others have asked on Stack Exchange, that why a certain phenomenon happens, in the response many (most) of the times it is said: "It happens to increase or maximize the entropy" or "It happens because in the final condition the extropy will be maximized". I have given some examples of such kind of questions and their responses, at the end of this post.
My question is: Can the maximization of entropy be the reason behind any phenomena to occur? Let me explain my question in more detail.
When I walk on the road on a sunny day, my shadow "accompanies" me. It happens all the time. It is statistically always true! But, we can never say that the motion of my shadow is the "Cause" behind my motion. Similarly, the increment or maximization of entropy of the universe is statistically observed to be always "Accompanied" by all the natural phenomena, but can that be the cause behind any natural phenomena to happen?
Do the atoms and molecules of a system somehow collectively "Know" (or programmed) that they together have to maximize the entropy? I doubt that!
As I understand, the atoms and molecules of a system just interact with each other with some forces and show some collective behavior. The only thing they experience is some "Interaction Force". If we consider this understanding to be right, then only the interaction forces can be the "cause" behind any natural phenomena.
Another argument is, maximization of entropy is a condition which still has to come in the future in a system, and if we assume it to be the cause, then there are again two more problems:
How can the effect precede the cause?
In this kind of line of thought, it is assumed that atoms and molecules already know or are programmed in some way to achieve a certain future. How is that possible?
In summary, in the explanation of any natural phenomena, I think, we cannot just stop at saying that since the entropy will be maximized in a certain direction so the system will move in that direction! There must be some even deeper or fundamental "Cause" than "Entropy Maximization" for that system to behave in a certain way.
The following are some posts which emphasis on "Entropy Maximation" to be the "Cause" behind certain phenomena.
Why do bodies tend to attain thermal equilibrium?
And there can be many more examples.
Answer
For this subject I can recommend the following book by P W Atkins 'The second law' (1984)
That book is written to be accessible to a large audience.
Let me first describe a particular demonstration that is in that book.
Take a grid of cells, 5 by 10 is large enough. Place a colored marker on the cells of a 5 by 5 square at one end of the grid, and a different colored marker on the 25 cells of the other end of the grid. Let's call the colors 'red' and 'white'.
The you start a process of random exchange of two adjacent markers. At the start that will mostly exchange markers of the same color. Over time the markers become more and more mixed.
The way to quantify this tendency towards mixed state is to count the number of states. In the total space of all possible states the states with the markers mixed outnumber the states with the markers significantely separated - by far.
I remember witnessing a demonstration that the above abstract example is a close analogy to.
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. Nitrogen dioxide is denser than air.
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 quantitively. 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 final temperature of the combined cases will be a bit lower than the starting temperature. That is, some kinetic energy has been converted to gravitational potential energy.
I think the above example counts as a case of probability acting as a causal agent.
Another example, in my opinion, is buildup of osmotic pressure, which I wrote about in an answer to a question titled Details of forces involved in osmosis at a microscopic level
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