
What is entropy and why does it always increase?
Entropy is a measure for how randomly distributed particles and energy within a system are. For any given mixture of different elements, it is highest when all atoms are completely mixed across the entire space and all energy is evenly distributed heat. For example, if I had a mixture of the noble gasses Helium and Neon, entropy would be lower than it could be if the Helium atoms were all on one side of the system (for example the volume within a glass cube) while the Neon atoms were all on the other side. It would also be lower than it could be if it contained some energy that was different to evenly distributed heat, for example if the Helium atoms had a higher temperature than the Neon atoms or if they had kinetic energy, i. e. if my clump of helium atoms was moving together in a specific direction, for example because I launched it into the glass cube in some way.
Of course, what would happen in all these cases is that the system would quickly approach maximum entropy. The moving clump of helium atoms would collide with Neon atoms and get scattered until all atoms would fly around randomly, which is heat, not kinetic energy. Similarly, the hotter Helium atoms would randomly collide with the cooler Neon atoms until they all have the same speed of randomly flying around, i. e. the same temperature (thermal equilibrium). And if I had each element on one side in the beginning, randomly flying around would mix them up, similar to how if I shook a glass of red and blue marbles where in the beginning the red marbles form a layer on top of the blue ones, they would also mix.
All of this is because everything moves around randomly. This will result in the most likely assortment of particles and energy prevailing. Entropy is a measure of how likely an assortment of particles and energy is. An increase in entropy means a change towards this more likely assortment. We always expect the likely thing to happen because of the huge numbers and small time frames involved.
If I threw two dice once, I would not be too surprised if they both showed a six. However, if I threw a hundred thousand dice at once or the two dice fifty thousand times, I would not believe my eyes if they all showed a six. Instead, I would expect them to be evenly distributed over all six possible results. This is known as the law of large numbers in probability theory.
Now, particles are far more numerous than these hundred thousand dice. Just 4 grams of Helium contain about 6.022*10²³ (one mole of) atoms! That means about 600 sextillions.
So, while it would be theoretically possible that in their random movements, all these atoms move in a way that lets them stay together instead of mixing with the neon particles, it is insanely unlikely. They all would have to move to the inwards of the helium clump at the same time even though a lot of directions that would take them out of the clump are also possible. And even if I try this for the remaining age of the universe, it would be unlikely that I ever observe these 600 sextillion dice always showing a six at the same time, i. e. stay together. And the Neon atoms would also have to do that at the same time in order to prevent mixing.
In this sense, the famous Second Law of Thermodynamics, which states that entropy always has to increase, can be rephrased to say that more likely things are for all intents and purposes certain to happen if the number is large enough. Which it is even for numbers of particles that seem small from our everyday sense of scale, like 4 grams of Helium. A single human contains far more particles, and anything going on in politics will affect humans and landscapes far larger in scale than this single human.
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