Entropy is a word that gets thrown around a lot - but what does it mean? Let's clear up a few misconceptions. Entropy is NOT disorder. It does NOT measure randomness. These are good metaphors - but ultimately misleading as both terms are subjective and not a true measure of entropy.
Entropy helps to explain why physical processes go in one direction, but not the other. For example, why your ice cream melts on a sunny day instead of getting colder.
To help get your head around this concept, we need to talk about energy and probability. And crack open the Lego.
Energy moves around in discrete packages called "quanta". Here's Ironman with four "quanta" of energy.
And here's a Lego representation of two solids. Each solid has four atoms (the red blocks) and four atomic bonds (the connecting white blocks). Energy is stored in these white atomic bonds.
There are many different ways that the four quanta of energy could be stored in the two solids.
The most probable energy configuration is that the solids have two quanta of energy each.
It's a bit like when you throw two dice. There is only one possible way to get a score of two (1+1) or a score of 12 (6+6). But to get a score of seven there are six possibilities (1+6, 6+1, 2+5, 5+2, 3+4, 4+3), or to get an eight there are five possibilities (2+6, 6+2, 3+5, 5+3, 4+4).
In entropy terms, then this is like saying a seven has the highest entropy. Because it's the most likely configuration when throwing two dice.
Back to the Lego solids. Statistically, we are more likely to have two quanta of energy in each solid. It's the most likely configuration. So, this configuration has the highest entropy.
Entropy is a direct measure of each energy configuration's probability.
In our example, low entropy means the energy is concentrated in one solid. High entropy means the energy is spread out across the two solids.
So, why does my ice cream always melt in the Sun?
Because energy is statistically more likely to disperse. The energy configuration with two quanta of energy in each solid is most likely.
So, systems move from low to high entropy because dispersed systems of energy are more likely.
In the Lego example, you could argue that there is still a small chance that a system could move from high to low entropy. All the quanta of energy could move from being equally divided between two solids, to all four quanta existing in one solid.
If we scale up to ice cream on a sunny day, that means that your ice cream could, theoretically, get colder once it's been served.
Energy from the cold ice cream could move to the warmer air surrounding your ice cream.
And your ice cream gets colder.
But this never happens. This is because your ice cream has more than eight atoms, eight atomic bonds and four quanta of energy floating around than the simplified example I gave.
Think about it.
Let's go back to the dice. There are 36 possible outcomes when you roll two dice. There are 216 possible outcomes when you roll three dice. With six dice, there are 46,656 combinations. And so on.
When we move up to scales where we have billions upon billions of atoms, bonds and energy quanta, then the chance of a cold object getting colder is so tiny that it never happens.
It would be like throwing only ones with billions of dice.
So, your ice cream melts because this state has more dispersed energy than the original fresh-from-the-freezer ice cream.
A shift from low to high entropy (and a melted ice cream) is statistically more likely.
Extra reading and watching
I'd really recommend this TEDEd talk on entropy, which prompted my Lego example. Entropy is also linked to the laws of thermodynamics, as this series of lectures from the Khan Academy explains. Its video on entropy goes into some great detail too:
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