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Eerie Entropy

Updated: Oct 8, 2023

Author: Arpan Dey

Thermodynamics, according to many experts in the field of physics, cannot be overthrown. From classical mechanics to quantum mechanics, no theory is 100% accurate. But it is a different story with thermodynamics. The principles of thermodynamics are fundamental. For instance, we may come to know, in the future, that quantum mechanical description of nature is indeed not completely accurate. But it would be a very difficult day for physicists if we find that the second law of thermodynamics is invalid. If we find it is so, we have to start physics from scratch!

What is the second law of thermodynamics? Simply put, it says that everything tends toward equilibrium. In other words, heat will always flow from a hotter object to a colder one, and never the reverse. Machines will always get inefficient over time due to the increasing amount of energy lost to the surroundings. You get the idea.

Entropy can be defined as being directly proportional to the number of ways a particular state can be achieved. In our universe, entropy increases with time. Entropy is increasing in our universe is itself a testimony to the fact that we started off in an orderly state, i.e., at low entropy. It seems reasonable to assume that entropy is a measure of disorder but that is not exactly so. For instance, if we have 5 differently-colored balls and 2 jars, then the lowest entropy state would be achieved if we keep all 5 balls in 1 jar and thus, no balls in the other. This state is not an equilibrium, obviously, for the concentration of the balls is more on one side. (An equilibrium state can’t be achieved in this state, as that would require each jar to have 2.5 balls in it!) If we decide to keep 2 balls in 1 jar and 3 in the other, by taking into account the 5 different colors, there are many different ways we could achieve this state, and thus in this case, the entropy of the system is more than in the previous case, when there were only 2 possible ways to achieve our state (i.e., either all the balls in the first jar or in the second jar, while keeping the other jar(s) empty). As the second case is more toward equilibrium and stability, and as everything in this universe tends to remain stable, entropy increases in our universe.

Entropy always increases, at least in our universe. For instance, even if we try to compress some atoms in a smaller space so that the number of possible arrangements (and consequently, entropy) decreases, the energy of the atoms will increase, increasing the number of possible arrangements. Even if we forcibly prevent a system to reach equilibrium, i.e., highest entropy state, we must be aware of the states of the particles to achieve the feat. Here, the information in our brains is equivalent to entropy. And even if we try to forget this information, the temperature around our brain increases, thus not letting entropy to decrease.

At the very beginning, when a tiny fluctuation in the vacuum gave rise to an infinitely-dense point that began to expand to form this universe, the Big Bang state must have been symmetrical because the probability of asymmetry in such a dense, tiny and fundamental state is negligibly small. Yet that stage was clearly not in equilibrium to the surroundings (i.e., zero energy vacuum). Thus, entropy was low then, for it was a fundamental state. Over time, with the expansion of the universe, this system has advanced more toward equilibrium, and has lost symmetry in the process.

It is another great puzzle that the laws of physics make no distinction between the past and the future, meaning it is possible for time to ‘run backward’. But we don’t see a broken cup pick itself up from the floor and repair itself. This leaves open the possibility of a CPT(Charge-Parity-Time)-reversed universe, for if all of these are reversed, the laws of physics simply don’t change.

Ludwig Boltzmann assumed that our universe began in a very unlikely state. Entropy increases both into the past and the future, and we are, thus, existing on the vertex of a lower ‘V’ shape from the original equilibrium state, in an entropy-time graph. Our universe, in this view, could’ve come into existence just a moment ago, complete with traces of the past of a greater universe. In statistical mechanics, there is a small but non-zero chance that some gas molecules in an open container do not come out of it, even when the surroundings are devoid of any gas molecules. This doesn’t generally happen, for everything will tend to achieve an equilibrium state. But if we wait long enough, at one time such things must occur for there is still a probability for them to occur, no matter how small. Given enough time, we may see some atoms in a system by themselves huddle in a corner of the system, and not move. In such cases, as the system was more in equilibrium before the unlikely state was achieved, entropy also increases into the past.

“That in nature the transition from a probable to an improbable state does not take place as often as the converse, can be explained by assuming a very improbable initial state of the entire universe surrounding us. This is a reasonable assumption to make, since it enables us to explain the facts of experience, and one should not expect to be able to deduce it from anything more fundamental”, said Ludwig Boltzmann.

In conclusion, entropy is arguably the most important concept of modern physics. If you are still not convinced, just know that today physicists debate over whether gravity is a fundamental force at all! What is gravity then? An emergent force, that arises in a system and follows the laws of thermodynamics. Or an "entropic force"!

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