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:

  1. How can the effect precede the cause?

  2. 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?

Why most distribution curves are bell shaped? Is there any physical law that leads the curves to take that shape?

And there can be many more examples.

  • 1
    $\begingroup$ It is because of random changes that entropy tends to its maximal value. That is the overwhelmingly most likely configuration, the state with most microstates. $\endgroup$
    – user137289
    Commented Jan 4, 2020 at 15:41

2 Answers 2


You are right that the "maximization of entropy" is not the cause of anything; entropy is an emergent phenomenon, meaning that it is a result of the behavior of an underlying system, in this case some collective. The power of the concept "entropy" is that it is independent of the underlying "substrate" — all collectives follow a path to higher entropy, independent of their specific constituents. The idea to essentially look at collectives from a statistical point of view is so powerful because there is only a minimal set of assumptions about the behavior and interaction of the collective's constituents (if I'm not mistaken, random interaction is the only one). The concept of "entropy" therefore turns out to be a completely universal concept, including the literal sense of the word. (In that it perhaps resembles another abstract concept, that of evolution in a broader sense.)

So if it is never the cause of anything but, on the contrary, always a consequence, why do we sometimes use entropy to explain behavior? Because the rules we found how collectives behave can be used to predict their behavior without having to go through all the gritty details. If we want to predict the eventual temperature distribution in a system or the end state of two gases after we remove a membrane we can simply say "the state will be X because that's the maximum entropy", without simulating the trajectory of $10^{25}$ molecules.

This mental "inversion" is the common way we think in classical physics. We can predict that a ball rolling on an uneven surface will come to rest in a local depression, a place of minimum altitude. Isn't that obvious? It will minimize its potential energy! But of course the ball knows nothing about potential energy or the surface topology beyond the point it is currently on. Both are abstract concepts we use to simplify our mental model of the world. If we are allowed to stay within the realm of Newtonian physics, the ball really only "cares" about the gravitational vector and the surface inclination at each point in time and space and some friction, and its velocity changes according to the resulting forces.

Even though the ball is really very dumb we may say "it wants to be to be at the point of lowest potential energy", even though this is the result of the underlying physics, not the cause.

Similarly, we say "the system moves towards thermodynamic equilibrium", even though this is the result of the underlying physics, not the cause. It is just that it is always the case, and cannot be any other way because the concept expresses a fundamental insight into the behavior of collectives.1

1 I really would like to stress the similarity to the concept of evolution again. Both entropy and evolution are very general insights into the emergent behavior of systems. Both predict behavior which appears to imbue the "agents" (gas molecules, organisms) with an insight into the big picture they clearly don't possess. In the case of evolution similar misconceptions as the one you questioned here are typically brought forward by creationists ("this directed development obviously shows intent"). The two concepts are also related: If we abstract the concept of evolution even further from the biological requirements of mutation, selection, procreation simply into "development in the face of interaction" it becomes a general concept for evolving (sic) systems. Biological species are around because they survived; but anything we see around us is there because it didn't go away yet as well. The things we see are either very long-lived (sand, mountains, stars) or they reproduce (organisms, tectonic plates). Everything that does neither is simply not there any longer. Thermodynamics then is the rule set for the evolution of dynamic systems. The system states we observe are simply the ones which prevail. A system's path of development towards higher entropy is not any more "directed" or "intentional" than the biological evolution towards better adaptation — it is simply the selection of a most likely path under the given circumstances.
  • $\begingroup$ This is a pretty nice explanation of the distinction between these two types of theories, which are often called "principle theories" and "constructive theories", following Einstein's philosophy of science. He had some interesting views on the subject, which I definitely recommend to people to read. $\endgroup$
    – Noldorin
    Commented Nov 19, 2021 at 2:49

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

Later edit:
Some additional remarks about how equilibrium comes about in various circumstances.

In the case of gaseous diffusion the end state is not quite uniform. Due to gravity there is a slight bias. The state that the system develops to is one with a slight gradient, with the heavier molecules slightly overrepresented at the bottom, and underrepresented at the top.

Earth gravity is 1 G of acceleration, which gives a very weak bias only. The amount of bias can be increased by increasing the G-load. The most extreme case of that is ultra-centrifugation. The uranium-hexafluoride molecules are gaseous. The ultra-centrifuge sets up a very high G-load. The mass difference between the Uranium isotopes is very small, but at the extreme G-load of ultra-centrifugation a bias in distribution is created. Uranium-hexafluoride siphoned off at the inside diameter is somewhat depleted of the heavier isotope, Uranium-hexafluoride siphoned off at the outside diameter is somewhat enriched with the heavier isotope. Multiple ultra-centrifuges are run in series, the Uranium-hexafluoride being led from stage to stage, until the desired level of separation is achieved.

In the case of suspension in liquid:
In the blood many of the large molecules remain in suspension. The G-load of 1 G is not enough to make those molecules go out of suspension. That is under a G-load of 1 G the probability effect is dominant. So biologists use a centrifuge. With a sufficiently high G-load large molecules do settle.

For very large objects, such as grains of sand: a G-load of 1 G is sufficient to make them go out of suspension. On the other hand, for a fine dust 1 G is not enough. Example: the black pigment of black ink is a fine dust. The pigment of black ink does not settle.

  • $\begingroup$ Wonderful example. Probability acting as a casual agent is mind blowing. $\endgroup$ Commented Jan 4, 2020 at 19:34
  • $\begingroup$ How is the book "Entropy Demystified" by Arieh Ben Niam? $\endgroup$ Commented Jan 4, 2020 at 20:15
  • $\begingroup$ I don't buy it. The collective states are emergent; they are not the cause of anything, to the contrary. $\endgroup$ Commented Jan 9, 2020 at 22:05
  • $\begingroup$ If I scoop out a jam jar full of river water and set it down, the sediment and particulate therein will settle in neat bands according to density. Intuitively I feel the difference is liquid vs gaseous, but nonetheless why is this there change from a more to less mixed state in this case? By the above implied definition, this is increasing order, decreasing entropy. Is entropy increasing somewhere else somehow? Why doesn't it in the gaseous case? $\endgroup$
    – benxyzzy
    Commented Sep 16, 2020 at 17:08
  • 1
    $\begingroup$ @benxyzzy I have added some remarks thad address your questions. $\endgroup$
    – Cleonis
    Commented Sep 16, 2020 at 21:23

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